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.