This is not your everyday chocolate cake. It's a showstopper—very tall and much more of a bakery-style cake than a cake from a box. The frosting has both melted chocolate for smoothness and cocoa for depth of flavor.
For the cake: Arrange a rack in the center of oven and preheat to 350 degrees F. Lightly coat two 9-inch round cake pans with nonstick cooking spray. Line the bottoms with parchment paper rounds and lightly coat the paper with nonstick spray. Dust the bottom and sides of each pan with Dutch-process cocoa powder, tapping out excess.
Sift the cocoa powder, flour, baking soda and baking powder into the bowl of a stand mixer. Beat on low speed to combine. Add the eggs, egg yolks, brown sugar, sour cream, oil, vanilla, salt and 1 cup of hot water. Beat on medium speed until completely smooth, about 3 minutes.
Scrape the batter evenly into the prepared pans. Smooth the tops. Bake, rotating the pans halfway through, until a tester inserted into the centers comes out clean, 35 to 45 minutes. Transfer the pans to a wire rack and let the cakes cool for 30 minutes. Run a knife around the sides of the cakes and invert onto the wire rack. Remove the parchment and let the cakes cool completely.
Trim the domes of the cake rounds with a large serrated knife so the tops are flat.
For the frosting: Melt the chocolate in a medium heatproof bowl set over simmering water in a medium saucepan. Remove from the simmering water and let it cool to room temperature, about 30 minutes.
Beat the butter and salt in a large bowl with an electric mixer on high speed until light and fluffy, about 2 minutes. Reduce the speed to low, drizzle in the chocolate and beat until completely blended. Gradually beat in the confectioners' sugar, cocoa powder and vanilla. Increase the speed to high and beat until light and fluffy, about 2 minutes.
To assemble the cake: Place one cake, cut-side down, on a platter. Spread 1 1/2 cups of the frosting evenly over the top. Place the remaining cake, cut-side down, on top. Spread the top with 1 1/2 cups of the frosting. Frost the sides of the cake with 3/4 cup of the frosting and smooth out completely to make an even crumb coat. (It's ok if some of the cake shows through. This is just a base layer.) Refrigerate for 30 minutes to let the frosting set.
Spread the remaining frosting over the top and sides, swirling decoratively.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.
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