Make the ganache: Heat the heavy cream, semisweet chocolate and espresso powder in a heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water), stirring, until the chocolate is melted and the ganache is smooth. Stir in the vanilla and coffee liqueur. Remove the bowl from the pan; set aside until cool and thick but still pourable, about 1 hour.
Meanwhile, make the filling: Put the milk chocolate in a microwave-safe bowl; microwave in 30-second intervals, stirring, until smooth. Let cool.
Beat the butter and salt in a large bowl with a mixer on medium speed until smooth and fluffy, 2 to 3 minutes. Add the melted milk chocolate and beat until combined. Gradually beat in the confectioners' sugar until smooth. Add the cocoa powder and vanilla, increase the mixer speed to medium high and beat until smooth, 2 to 3 minutes.
Assemble the cake: Put 1 chocolate cake layer on a platter; spread 3/4 cup filling on top. Top with a vanilla cake layer and spread with another 3/4 cup filling. Repeat to make 4 layers, ending with a vanilla cake layer. Spread the remaining filling on top and refrigerate until firm, at least 30 minutes. Pour the ganache over the cake, letting it drip down the sides. Let set at room temperature before slicing, about 30 minutes.
Basic Chocolate Cake:
Yield:two 9-inch cakes
Preheat the oven to 350 degrees F. Coat two 9-inch-round cake pans with cooking spray and line the bottoms with parchment paper.
Whisk the cocoa powder and 1 1/2 cups boiling water in a medium bowl until smooth; set aside. Whisk the flour, sugar, baking powder, baking soda and salt in a large bowl until combined. Add the eggs, vegetable oil, sour cream and vanilla and beat with a mixer on medium speed until smooth, about 1 minute. Reduce the mixer speed to low; beat in the cocoa mixture in a steady stream until just combined, then finish mixing with a rubber spatula. (The batter will be thin.)
Divide the batter between the prepared pans and tap the pans against the counter to help the batter settle. Bake until a toothpick inserted into the middle comes out clean, 30 to 40 minutes. Transfer to racks and let cool 10 minutes, then run a knife around the edge of the pans and turn the cakes out onto the racks to cool completely. Remove the parchment. Trim the tops of the cakes with a long serrated knife to make them level, if desired.
Basic Vanilla Cake:
Yield:two 9-inch cakes
Preheat the oven to 350 degrees F. Butter two 9-inch-round cake pans and line the bottoms with parchment paper; butter the parchment and dust the pans with flour, tapping out the excess.
Whisk 3 cups flour, the baking powder and salt in a bowl until combined. Beat 2 sticks butter and the sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Reduce the mixer speed to medium; beat in the eggs, one at a time, scraping down the bowl as needed. Beat in the vanilla. (The mixture may look separated at this point.)
Mix 1/2 cup water with the cream in a liquid measuring cup or bowl. Beat the flour mixture into the butter mixture in 3 batches, alternating with the cream mixture, beginning and ending with flour, until just smooth.
Divide the batter between the prepared pans. Bake until the cakes are lightly golden on top and the centers spring back when pressed, 25 to 30 minutes. Transfer to racks and let cool 10 minutes, then run a knife around the edge of the pans and turn the cakes out onto the racks to cool completely. Remove the parchment. Trim the tops of the cakes with a long serrated knife to make them level, if desired.