Preheat the oven to 350°F (175°C). Grease two 6-inch round cake pans with butter, line the bottoms with parchment paper rounds, and lightly dust the sides with flour or cocoa powder. Tap out any excess and set the pans aside.
In a large mixing bowl, whisk together the all-purpose flour, cocoa powder, cornstarch, baking soda, baking powder, salt, granulated sugar, and dark brown sugar until fully combined.
Add the eggs, sour cream, vegetable oil, and vanilla extract to the dry ingredients. Whisk until the mixture forms a thick, smooth batter.
In a measuring cup, dissolve the espresso powder in the boiling water. Pour the hot coffee mixture into the batter and whisk until fully incorporated. The batter will be thin, which is normal.
Evenly divide the batter between the prepared cake pans.
Bake the cakes in the center of the oven for 35 to 40 minutes, or until a skewer or toothpick inserted into the center of the cakes comes out clean or with just a few moist crumbs.
Let the cakes cool in the pans for 5 minutes, then turn them out onto a wire cooling rack. Allow the cakes to cool completely to room temperature before assembling and decorating.