1/2cupplus 3 tablespoons cocoa powder (equal parts unsweetened cocoa powder and Dutch-processed, meaning that you should use 1/4 cup plus 1 1/2 tablespoons natural cocoa powder and another 1/4 cup plus 1 1/2 tablespoons of Dutched cocoa powder)
1cup(2 sticks) unsalted butter, at room temperature
1cupunsweetened cocoa powder
1tablespoonplus 1 teaspoon light corn syrup
7cupsconfectioner's sugar
3 to 6tablespoonswhole milk, at room temperature
Instructions
For the Chocolate Sour Cream Cake
Preheat the oven to 350 (F). Coat two 9-inch round pans with nonstick cooking spray, and line the bottoms of the pans with parchment paper.
In a medium bowl, mix together 3/4 cup sour cream, 1/2 cup plus 3 tablespoons cocoa powder, 2 eggs, 2 egg yolks, and 1 1/2 teaspoons vanilla until smooth.
In the bowl of a stand mixer fitted with a paddle attachment, beat together 2 1/4 cups cake flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 3/4 teaspoon salt, and 1 3/4 cups granulated sugar on low speed just until blended.
Add 1 cup unsalted butter and half of the cocoa mixture (from the second step) to the flour mixture (from the third step) and beat until the dry ingredients are moist.
Increase the mixer speed to medium and beat until smooth, about 2 minutes. Gradually add the remaining cocoa mixture in 2 batches, beating well after each addition. Add 1/2 cup boiling water and beat until smooth.
Divide the batter equally between the prepared pans and smooth the tops with an offset spatula. Bake until a wooden pick inserted into the center comes out clean, about 30 to 35 minutes. Let the cakes cool in the pans for 10 minutes before turning them out onto a wire rack to cool completely. Remove the parchment paper.
For the Chocolate Buttercream
In the bowl of a stand mixer fitted with the paddle attachment, beat 6 ounces cream cheese and 4 teaspoons vanilla together on low speed until smooth. Increase the mixer speed to high. Add 1 cup butter and beat until incorporated, using a rubber spatula to scrape the bowl as necessary, about 1 minute.
Reduce the mixer speed to low and beat in 1 cup cocoa powder and 1 tablespoons plus 1 teaspoon light corn syrup. Add 7 cups confectioners' sugar and beat until blended. Add 3 to 6 tablespoons of whole milk, one tablespoon at a time, beating until the buttercream achieves a spreadable consistency. Set aside until ready to use.
Putting It All Together
When the cake is completely cooled, use a large serrated knife to cut each of the 2 layers in half to make 4 thin layers in total.
Place the first layer on a cake plate, and use an offset spatula to spread 1 cup of buttercream on top. Repeat with the next 2 layers.
Place the final cake layer on top and spread the remaining buttercream on the top and sides of the cake.