Ginger Basil Lemonade

We’ve been having temperatures between 28 and 38 (for the Celsius-impaired, that is 82 to 100 Fahrenheit) degrees every day since I got back from England. Whev. It’s tiring to be out in this kind of weather. But, on the plus side, it gave me an excuse to experiment with my recipe for ginger basil lemonade, and perfect it enough that I can post it here. Ginger and basil take regular, delicious lemonade and make it unbelievable.

This is literally the best lemonade I have ever had, and believe me, I’m a bit of a connoisseur. The ginger and basil just set off the lemon perfectly, and the resulting drink is less of a sweet treat than it is a delicious every-day drink. I like to have a glass after a hard day of teaching (more about that in a later post), before getting back to studying for prelims. Writing the word regular up there gave me topology-flashbacks. I can’t wait for when prelims are over, and I can start with some real graph theory work.

Ingredients (makes 10 cups of lemonade).
6 medium lemons, washed.
1 inch of ginger
10-15 fresh basil leaves
1/2-1 cup of sugar
3+6 cups of water

Start by peeling off the yellow part of the lemon peel. I recommend using a potato peeler, but you can also use a knife for this. Try to avoid the white rind, because it will make your lemonade bitter. Peel the ginger and cut into 4 or 5 large pieces. Place the lemon peel, ginger, basil leaves, sugar, and 3 cups of water in a pot. Bring to a boil, and let simmer for about 10 minutes.

In the meantime, press the lemon juice from the lemons into a large pitcher. Strain the lemon-ginger-basil syrup into the pitcher. Add the remaining 6 cups of water. Chill overnight, and enjoy poured over ice.

PS: Does anyone know how to take good pictures of drinks? Mine always come out terrible, and I have no idea what to put in the background…

Normal spanning trees and swirl cupcakes

Today I had my last official class of my first year, a topology class. We talked about homology invariants and ate the chocolate vanilla swirl cupcakes I made for the occasion. It’s weird that I don’t have any more classes left. I almost even miss analysis homeworks. I have plenty of things to keep myself occupied until August though. Tomorrow I have a mandatory research ethics course to attend. 8 hours of listening to someone talk about how we shouldn’t experiment on people without the permission of the ethics review board. I imagine it will be moderately interesting, at best. Well, unless I come up with some experiment like these two mathematicians, courtesy of Spiked Math.

Today I want to share some interesting graph theory. Given a connected graph G, we can find a spanning tree T. This can be proved by simple induction. However, it is also true that we can find a normal spanning tree in any connected graph.

Given a tree fix a vertex called the root, r, of the tree. Next, we define a partial order on the vertex set of G by if x is in the unique path from r to y. This is the partial tree-order associated with r.

We call a rooted tree with root r normal in G if every pair of vertices that are adjacent in G is comparable in the tree-order associated with r.

Theorem. Every connected graph G has a normal spanning tree.

The reason I wanted to share this result with you is because it has a beautiful inductive proof where we induct on the number of edges. Think about it for a few minues before you scroll down to see.

Proof. For the base case, consider a connected graph on one edge. Clearly, this graph is , which is its own normal spanning tree. Now suppose every graph on n edges has a normal spanning tree. Then there are three cases for the inductive step: if we add another vertex, then the new normal spanning tree will be the old one joined with the new edge. Since there are no more edges connected to the new edge, this is still a normal spanning tree.

In the second case, we add the new edge to the old graph, but it does not affect the partial order on the normal spanning tree, so we are done.

The final case is the tricky one: suppose that the new edge connects two vertices that are not comparable in the tree order. In this case, we create a new spanning tree by adding in the new edge, connecting two branches of the spanning tree. Then we pick one of the original branches and delete the edge in it closest to the root of the tree. Then we have a spanning tree again, and it is normal. Q.E.D.

Oh, and those cupcakes I mentioned? I used a recipe I found on JoyOfBaking. This is one of the best sites I have ever found for basic recipes, like vanilla cupcakes, brownies, red velvet cake, peanut butter cookies, and so on. I highly recommend it. I separated the frosting in two bowls, melted a handful of dark chocolate chips and whipped into one of them to make half chocolate and half vanilla frosting. And here’s the end result:

Place a teaspoon of each frosting on the cupcakes like this

Use the tip of a butterknife to swirl the colours into each other

A closeup of the result

Bacon and egg cupcakes

Time for a new recipe. I’ve been trying to find a nice snack to have before working out, or for those mornings when snoozing 10 times is more appealing than getting up and making a proper breakfast. I decided that eggs and bacon were a given, and there should be something green in there too, at least for show. These freeze really well, and can be defrosted in the microwave in about two minutes. Otherwise they last for 4-5 days in the fridge (unless you’ve eaten all of them by then). I keep some in the freezer in the graduate kitchen in case I stay late and need a snack, or need something to eat before going to the gym.

The recipe is really easy, you can expect the prep to take about 10-15 minutes. This depends on how good you are at shaping the bacon pieces. It gets a little messy, but it is oh so worth it when you can grab one or two of these on a stressful morning.

The recipe calls for medium eggs: this is to keep the cupcake molds from overflowing. If you have large eggs I would not crack straight into the cupcake tray, but instead into a small ramekin. Then use a spoon to place a yolk in each mold, and add as much white as you can fit without the cupcake overflowing. These will not rise, and will in fact shrink a little as they cook, so you can fill them to the brim. The final tricky step is to be very careful when placing them in the oven, so that the broccoli doesn’t fall over. Then you have a perfect breakfast or pre workout snack for the rest of the week, with minimum work. Enjoy!

Ingredients (makes 6 servings)

12 rashers of bacon
12 medium eggs
12 small bouquets of frozen broccoli
Salt, pepper and smoked paprika powder
Cooking spray

Preheat the oven to 350 degrees. Lightly spray a cupcake tray with cooking spray. Place a rasher of bacon in each cupcake mold, and add a broccoli bouquet to each mold. Very gently crack an egg into each cupcake. Add a pinch of salt, a twist of pepper and a sprinkle of smoked paprika powder. Bake for 25-30 minutes, or until firm.

Angel hair pasta with pea pesto and leftover turkey

Right before Christmas I found out that my university hands out turkeys to all their employees, so I have the freezer full of frozen cooked turkey. It’s turning out to be very convenient. New Year’s Day is probably the laziest day of the year for me, and since I hadn’t done anything by last night, I decided to come up with a quick and easy dinner recipe. It turned out absolutely delicious, and the best part is that it can be done in 15-20 minutes, depending on how quickly your stove boils pasta water! All you need is a blender / immersion blender / food processor and some leftover cooked protein. This is turning into a new working day favourite for me.

Ingredients (2 servings)

• 2 servings angel hair spaghetti
• 3/4 cup of deep-frozen peas
• 1/4 cup of white wine (or chicken stock, if you don’t have wine)
• 1 small peeled clove of garlic
• 1 tbsp dried basil
• 1/2 tsp Dijon mustard
• 1 egg yolk
• 3/4 cup shredded cooked turkey (or other cooked protein of your choice)

Start the pasta water. Dump all the ingredients except for the pasta and the turkey in a blender. Pulse for 30 seconds or until smooth. Boil the pasta according to the instructions on the package. Drain the pasta and pour the pesto over it. Add the turkey and place the pan over medium heat for a couple of minutes, until everything is warm. Serve with sharp cheddar cheese.

Mahi Mahi with Tomatoes and Peas

Right before Christmas, I usually crave fish and vegetables. I guess it’s my body preparing for the onslaught of meat, gravy and pie that is coming. The other day, I improvised this recipe and decided that I had to share it. It’s quick, easy, delicious and healthy (well, minus the bacon).

Ingredients:

• 1 piece mahi mahi
• 1 slice of bacon
• ~15 cherry tomatoes
• 1 small clove of garlic
• A handful of peas
• 1/4 cup white wine
• Salt
• Black pepper
• Oregano

Start by frying the bacon, on medium heat, until it is crispy. Meanwhile, chop the garlic and halve the tomatoes.

Pour the wine into a small pot and start simmering it with the garlic and a little bit of oregano. When the bacon is done, place it on a paper towel to remove excess fat. Pour out excess bacon fat from the pan, and start frying the mahi mahi, skin side down for about 3-4 minutes or until the skin is nice and crispy. Add the tomatoes to the wine and spices. Generously salt and pepper the top of the mahi mahi before flipping it over.

Let the fish finish cooking for another 3-4 minutes. Add the peas to the tomatoes and let it simmer for a few more minutes. You want the tomatoes to be cooked, but not falling apart. Place the fish and vegetable on a plate, and crumble the bacon slice over it. Enjoy!

Christmas brownies

It would seem I have lapsed in my blogging. But, this time I’m making up for it with a recipe for Christmas brownies. My first semester of grad school is over (at least until the grades are released) and I decided it called for brownies. Then I had some more realisations: it is almost Christmas, and the best part of Christmas is peppermint mochas. So I decided to modify my tried and true briwnie recipe into peppermint mocha brownies. I also decided that these brownies needed a little extra in the form of spiced rum. As always with brownies, you need to use a good quality chocolate that you enjoy eating on its own, as this is what your brownies will taste like. I used Ghiradelli’s 70% cocoa chocolate chips for mine, and it turned out delicious.

Ingredients for brownie:

• 4oz dark chocolate
• 1/2 cup butter
• 2 tsp instant coffee
• 1/2 tsp peppermint extract
• 2 tbsp dark, spiced rum
• 3/4 cup granulated sugar
• 2 eggs
• 3/4 cup flour

Ingredients for topping:

• 4oz dark chocolate
• 2tbsp heavy cream
• 1 candy cane, crushed

Preheat the oven to 325 degrees Fahrenheit. Melt the chocolate and butter in a pot over low heat. Stir carefully to make sure it doesn’t burn (if you are worried, melt it in a steel bowl over a water bath). Take the pan off the heat and stir in the instant coffee, peppermint extract and rum. Add in the sugar, and then the eggs, mixing carefully after each addition. Finally add in the flour. Pour the batter into a 9×9 inch brownie pan and bake for 20-25 minutes or until a toothpick inserted in the center comes out with a few moist crumbs. Closer to 20 minutes will yield a more fudge-like brownie, and closer to 25 will give you a more cake-like one. Let the brownie cool completely before attempting to decorate it.

When it is cooled, melt the dark chocolate (on the stove or in the microwave) and stir in the heavy cream. Spread this over the brownie, sprinkle the crushed candy cane over it and then chill for about an hour. Cut into 9-16 pieces, depending on how big you like your brownies (the correct answer is as big as possible without getting sick from too much sugar). Serve room temperature or cold, possibly with some vanilla ice cream or whipped cream.

I didn’t realise how much a crushed candy cane sprinkled over the chocolate topping would add to the cake until after I took the pictures: hence the lack of red and white sprinkles there.

These are the perfect thing to enjoy on a rainy December evening with a good book. They are dense, chocolatey and with a certain oomph from the rum, coffee and peppermint. I’m currently obsessed with Ken Follett, and if my grad student budget allowed me to I would have bought all of his books as a Christmas present to myself. As it stands I have to ration them a little. But now I’m off to find any brownies my roommate and boyfriend haven’t eaten and finish Winter of the World. Enjoy your brownies!

Pasta with Peaches and Chicken

I finally moved in to my new apartment here a few days ago. The kitchen is amazing, so the first night I was here, I cooked a proper meal. I found some very nice peaches earlier that day, so I knew I wanted to incorporate those, and I wanted something a little bit spicy. This is what I came up with:

Ingredients:

• 4 portions of rigatoni (or any other pasta you prefer)
• 4 chicken thighs
• 2 large peaches
• 2 tomatoes
• 1tsp sriracha sauce
• 1tsp honey
• Chicken bouillon (corresponding to one cube)
• Basil
• Oregano
• Salt
• Pepper

Start by roughly chopping the peaches and the tomatoes. Put these in a small pan with a few tablespoons of water over medium heat. Let them simmer while you prepare the rest of the meal. Start the pasta water. Rub the chicken thighs with a few drops of sriracha and the basil and herbs. Start heating up a frying pan over medium heat with some cooking spray or butter, depending or what you prefer. While it’s heating up, add some spices to the tomatoes and peaches: about 5 drops of sriracha, or to taste, a teaspoon each of basil and oregano and the chicken bouillon. When the frying pan is hot, place the chicken thighs in it and let them fry for about 3-5 minutes or until they have a nice colour. Flip them over, and drizzle a little bit of honey on each thigh, turn the heat down to low and let them finish cooking (roughly 10 minutes). Now would be the time to add the pasta to the boiling water, and if it’s not boiling, take a break and come back when it is. Pour the sauce into a blender and mix until smooth. Pour back into the pan and salt and pepper it to taste. Drain the pasta when it’s cooked. Mix in roughly a third of the sauce, place pasta on plates, top with a chicken thigh and some more sauce. Enjoy!

 

This sauce is one of my new favourite foods. I would recommend doing a big batch, because it will just disappear. If there are an leftovers, I fond that it’s delicious cold as a pasta salad with some added spinach leaves and the chicken diced.

Simple Birthday Cake

For my birthday a few days ago (finally 21!), I made a delicious cake, featuring some of my current favorite tastes. The first layer is a brownie like cake, covered in a very tart lime mousse, and then with a pile of strawberries on top. This cake takes a little while to make, mostly because everything has to cool and set in between layers. It’s very simple though, as long as you’re gentle with the mousse. It would be a good idea to make the brownie cake the night before and the mousse in the morning.

For the brownie cake you will need:

• 100 grams butter
• 4 tablespoons cocoa powder
• 1 pinch of salt
• 1 teaspoon vanilla extract
• 3 deciliters granulated sugar
• 1.5 deciliters flour
• 2 eggs

Set the oven to 160 degrees Celsius. Melt the butter. While it cools slightly, mix all the dry ingredients in a large bowl. Stir in the eggs one by one and then the butter. Transfer to a buttered springform pan (24 – 28 cm diameter), dusted with cocoa powder, and bake for approximately 35 minutes. A toothpick inserted in the center should still be sticky. This cake needs to cool completely before the next step. I would recommend removing the edge of the springform pan and cleaning it before making the mousse, to end up with a nice, clean cake.

The mousse is a little bit harder to make, but still fairly simple. You will need:

• 2 gelatin leaves
• 2 deciliters heavy cream
• 2 eggs, separated
• The juice of 3 limes
• 3/4 deciliter granulated sugar

Soak the gelatin leaves in cold water. Whip the cream until soft peaks form. Gently fold the egg yolks into the cream. In a separate bowl, whip the egg whites until hard peaks form. Heat up the lime juice mixed with the sugar, but don’t let it boil. Stir the gelatin leaves into the lime juice. Fold the lime mixture into the whipped cream. Finally, fold in the egg whites, a little at a time, very gently. Spread this mixture on the cake and let it set in the fridge for at least 3 hours.

• 2 cups of sliced strawberries
• (Powdered sugar)

To serve, cover the top with sliced strawberries and (depending on how sweet they are) dust some powdered sugar over the cake. Enjoy!