Instructions

1. Make the chocolate filling: In a medium heavy-bottomed saucepan, whisk 1⁄4 cup sugar with 1 tbsp. plus 1 tsp. cornstarch, cocoa powder, and 1 tsp. salt. Whisk in 1 egg until smooth, then whisk in the cream, 3⁄4 cup milk, and seeds from 1⁄2 the vanilla bean. Place the pan over medium heat and cook, stirring constantly, until the filling thickens to the consistency of loose pudding, 8 to 10 minutes. Remove the pan from the heat and stir in the chocolate and 2 tbsp. cubed butter until smooth. Scrape the filling through a fine sieve into a bowl. Press a sheet of plastic wrap directly onto the surface of the filling and refrigerate until chilled and thickened, at least 4 hours.
2. Make the lemon curd filling: In a medium heavy-bottomed saucepan, whisk 1⁄2 cup sugar with 1⁄2 tsp. salt, 3 whole eggs, and 4 egg yolks until smooth, then whisk in the lemon zest and juice. Place the pan over medium heat and cook, stirring constantly, until the filling thickens to the consistency of loose pudding, about 5 minutes. Remove the pan from the heat and stir in 4 tbsp. cubed butter until smooth. Scrape the filling through a fine sieve into a bowl. Press a sheet of plastic wrap directly onto the surface of the filling and refrigerate until chilled and thickened, at least 4 hours.
3. Make the German buttercream: In a small heavy-bottomed saucepan, whisk 1⁄2 cup plus 2 tbsp. sugar with 1 tbsp. plus 1 1⁄2 tsp. cornstarch, 1 whole egg and 1 egg yolk, and remaining vanilla seeds until smooth, then whisk in the milk. Place the pan over medium heat and cook, stirring constantly, until the mixture thickens to the consistency of loose pudding, 6 to 8 minutes. Remove the pan from the heat and scrape the pudding through a fine sieve into a bowl. Press a sheet of plastic wrap directly onto the surface of the pudding and refrigerate until chilled and thickened, at least 2 hours.
4. Scrape the vanilla pudding into the bowl of a stand mixer fitted with a paddle and turn the mixer on to medium speed. Add 1 tablespoon of the softened butter and let the butter disappear into the pudding before adding another tablespoon. Repeat adding butter in this manner until the buttercream is smooth, pale, and fluffy, about 8 minutes from start to finish. (The buttercream will look curdled at first, but will smooth out by the time the last of the softened butter is added.) Scrape the buttercream into a bowl and cover with plastic wrap. If not using right away, refrigerate the buttercream for up to 5 days. Allow it to return to room temperature and beat it again in the stand mixer until fluffy before using.
5. Make the cake layers: Heat the oven to 375°. Line three 9-inch round cake pans with parchment paper circles and spray with nonstick baking spray. Sift the cake flour into a large bowl, then whisk in the baking powder. In a liquid measuring cup, whisk the buttermilk with the sour cream and vanilla until smooth. In the bowl of a stand mixer fitted with a paddle, cream 2 cups sugar with the butter and 3⁄4 tsp. salt on medium speed until pale and fluffy, about 3 minutes. Add the lemon zest followed by the egg yolks, adding one at a time, beating well after each addition until smooth. Reduce the mixer speed to low and alternately add the dry ingredients in 3 batches and the wet ingredients in 2 batches, beginning and ending with the dry ingredients, and beat until the batter just comes together. Using a rubber spatula, stir the batter again until smooth then scrape it into a large bowl. Clean and dry the bowl, return to the stand mixer, and fit with a whisk. Add the egg whites to the bowl and beat on medium-high speed until soft peaks form. Scrape the egg whites into the cake batter and gently fold until combined and smooth.
6. Divide the cake batter among the prepared cake pans and, using a small offset spatula, spread the batter evenly in each pan. Bake the cakes, rotating the pans halfway through cooking, until lightly browned and a toothpick inserted in the middle of each comes out clean, 20 to 22 minutes. Transfer the pans to a rack and let the cakes cool completely, then invert the cakes onto the rack and remove the parchment paper. Once the cakes are completely cooled, use a serrated knife to halve each horizontally to produce 6 cake layers total. While the cakes cool, make the simple syrup: In a small saucepan, combine the remaining 1 cup sugar with 1 cup water and bring to a boil, stirring to dissolve the sugar. Boil the syrup for 5 minutes, then remove from the heat and let cool completely.
7. Assemble the cake: Using a pastry brush, brush each cake layer with some of the simple syrup, discarding any leftover syrup. Using a small offset spatula, spread 3 cake layers each with one-third of the chocolate filling. Spread 2 cake layers each with half the lemon filling. Place 1 chocolate-covered cake layer on a cake stand, then quickly stack the remaining cake layers, alternating the lemon and chocolate fillings, and ending with the final, plain cake layer. Refrigerate the stacked cakes for 30 minutes. Using a small offset spatula spread the top and sides with the German buttercream until smooth. Place the cake in the freezer for 30 minutes.
8. While the cake is in the freezer, make the ganache: Place the chocolate in a medium bowl. In a small saucepan, heat the cream and 1⁄2 tsp. salt over medium until it begins to bubble at the edges. Remove the pan from the heat, pour the hot cream over the chocolate, and let stand, undisturbed, for 1 minute. Whisk the chocolate and cream from the center until the ganache is smooth and shiny. Remove the cake from the freezer and slowly pour the ganache over the top of the cake, using the offset spatula to guide and spread it over the side, until the cake is completely coated in the ganache. (You can also let the ganache drip down the side of the cake and set naturally, if you like.) Let the cake stand for about 10 minutes to allow the ganache to set before serving. Store the cake, wrapped in plastic wrap, in the refrigerator for up to 1 week (allow it to return to room temperature before serving).