Math & Cake: Chocolate Cake with Chocolate-Nutella Filling and Brown Butter Frangelico Frosting

Last week, I gave a talk about Math and Cake.  Ok, I had a fancier title, but my "side hobby" in mathematics is an area called fair division.  At some point in your life, you probably needed to fairly divide a candy bar or some other yummy treat between you and a friend:  one of you cut the treat in two, and the other got to choose first.  Fair!  But what do you do if there are three people? Or more?  My college adviser asked me this question on my very first day of college.  He does research in the area, and got me interested in the subject.  Extremely interesting mathematically, but also when else do I get to show pictures of all sorts of cake during a math lecture?!    See my book if you'd like to learn more about fair division and cake-cutting.

This is the cake I made for my talk.  It was sort of a prop, but I figured it'd give the audience something to look at if they zoned out for the math content!  No pictures of the inside of the cake unfortunately, but it went over very well.  Not a crumb left.

Chocolate Cake  (from Epicurious)
3 ounces fine-quality semisweet chocolate
1 1/2 cups hot brewed coffee (I used hazelnut coffee)
3 cups sugar
2 1/2 cups all-purpose flour
1 1/2 cups unsweetened cocoa powder (not Dutch processed)
2 teaspoons baking soda
3/4 teaspoon baking powder
1 1/4 teaspoons Kosher salt
3 large eggs
3/4 cup vegetable oil
1 1/2 cups well-shaken buttermilk
3/4 teaspoon vanilla extract

Preheat the oven to 300°F and spray 2 10" pans with baking spray (I used 2 9" pans and made an additional 3 inch cake; I've also used just the 2 9" pans before). Line bottoms with rounds of parchment paper and spray paper as well. 
 

Finely chop the chocolate and place in a medium bowl; pour hot coffee over the chocolate. Let stand for one minute, then stir until chocolate is melted and the mixture is smooth.

Whisk together the sugar, flour, cocoa powder, baking soda, baking powder, and salt in a large bowl.

In another large bowl, with an electric mixer, beat eggs until thickened slightly and lemon colored (about 3 minutes with a standing mixer or 5 minutes with a hand-held mixer).  Slowly add oil, buttermilk, vanilla, and melted chocolate mixture to eggs, beating until combined well.  Add sugar mixture and beat on medium speed until just combined well.

Divide batter between pans and bake in the middle of oven until a tester inserted in center comes out clean, 1 hour to 1 hour and 10 minutes.

Cool the cake layers completely in pans on racks. Run a thin knife around edges of pans and invert layers onto racks. Carefully remove parchment paper and cool layers completely.

This is a tall cake!



Chocolate & Nutella Frosting   (adapted from Chocolate Chocolate)

4 tablespoons unsalted butter
2 ounces unsweetened chocolate, melted and cooled to tepid
1/3 cup Nutella, depending on taste (the Nutella taste is somewhat mild)
Large pinch of Kosher salt
2 teaspoons vanilla extract
3 1/2 - 4 cups powdered sugar
1/2 cup milk, heated to tepid

Beat butter on medium speed for 1-2 minutes.

Blend in the melted chocolate, Nutella, salt, vanilla, 1/3 cup milk, and 2 1/2 cups powdered sugar.

Add in the rest of the milk; beat for 1 minute.

Add the rest of the powdered sugar; beat for 1 minute. Use more powdered sugar for a stiffer consistency, less for a softer consistency.

Refrigerate the frosting for 1-2 hours until spreadable.



Brown Butter Frosting (enough to frost/decorate a tall 9" 2-layer cake or a 3-layer 8" cake)


3 sticks butter, browned
1 1/2 pounds powdered sugar
6-8 tablespoons heavy cream
6-8 tablespoons Frangelico
Pinch of Kosher salt (optional)
1 tablespoon vanilla extract

Brown the butter, pour through a fine meshed sieve into a heatproof bowl, and set aside to cool.  Wait for it to cool completely.

Pour the cooled brown butter into mixer bowl (paddle attachment).  Add about 1/3 of the powdered sugar, and beat.  Add the caramel syrup, and continue beating. Add half the remaining powdered sugar, and beat. Add the 4 tablespoons (1/4 cup) of heavy cream, and beat until smooth.  Add more cream if you'd like the frosting to be softer, and more powdered sugar if you'd like it to be stiffer. Add salt if desired.

Refrigerate until ready to use.  Re-whip the frosting right before use. If it's been in the fridge awhile, you might need to let it sit at room temperature for an hour or so until it's soft enough to whip.


Assembly

Lay one of the chocolate cake layers on a cake board or plate.  Spread the chocolate frosting over the surface, leaving a half-inch border all around the outside.  You can also spread just half the frosting on this layer, and spread the rest on top.  You'll still cover the whole thing with the brown butter frosting.
Place the second cake layer on top of the first, and cover the whole cake with a crumb coat (very thin layer of frosting).  Be careful not to let your offset spatula touch the cake, or you'll get tons of chocolate crumbs in your frosting.  Place the cake in the fridge so that the crumb coat sets. You should be able to touch the cake gently without leaving any impression in the frosting.  Frost the cake again; it'll be easier this time with the crumb coat in place.  Use any leftover frosting to pipe shells, and/or tint some of the frosting and make roses. It's a good consistency as is, but if necessary (if it's very hot or humid out), add some more powdered sugar to make the frosting stiff enough for roses.

For instructions on how to do a crumb coat and how to decorate your cake, see King Arthur's online cake decorating tutorials.

For information on how to pipe roses, see Wilton's tutorial.  Or, take a class at your local Michael's.