For the cake: Preheat the oven to 350 degrees F. Butter and flour three 8-inch round cake pans, then line with parchment paper and butter the parchment. Set aside.
Using an electric mixer, beat together the brown sugar and butter in a mixing bowl. Add the eggs one at a time, beating well after each addition, then beat on high speed until light and fluffy.
In a small bowl, combine the instant espresso with just enough water to make a paste (approximately 1/4 cup); stir until the espresso has dissolved. Combine the flour, cocoa, baking soda and salt in a large bowl.
Turn the mixer to low speed and add the flour mixture in parts, alternating with the sour cream. Mix in the dissolved espresso. Stir in 1 cup boiling water until just blended. Divide the batter among the prepared pans and bake until a tester inserted in the middle comes out clean, about 35 minutes. Let the cakes cool in the pans for 15 minutes, then turn them out onto racks and allow to cool completely.
For the vanilla buttercream: Beat the butter and shortening with an electric mixer until fluffy, then slowly add the vanilla. Add in the confectioners' sugar 1 cup at a time, then turn the mixer to medium-high speed and beat for 5 minutes more.
To assemble: Level off the top of each cake layer with a serrated knife. Smear about 1 tablespoon buttercream on a cake plate to help secure the cake, then top with one of the cake layers. Add approximately 1 cup buttercream and spread it evenly around the top. Add a second cake layer and another cup of buttercream, again spreading all around to cover the top of the cake. Add the final cake layer. Working with small amounts of buttercream, cover the sides and top of the cake. Add interesting patterns with buttercream combs, or texture the outer part with a spatula. Serve immediately or cover to keep fresh.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.