For the cake:
1¼ cups (6¼ oz.) all-purpose flour
1 cup (3 oz.) unsweetened cocoa powder, plus more for dusting the pans
2 tsp. instant espresso or coffee powder
1 cup boiling water
½ cup sour cream
2 tsp. vanilla extract
1 cup (2 sticks) unsalted butter, at room temperature
1¾ cups (12¼ oz.) sugar
2 large eggs, at room temperature
1 tsp. baking soda
½ tsp. salt
For the frosting:
9.5 oz. bittersweet chocolate, finely chopped
6 oz. cream cheese, at room temperature
6 tbsp. unsalted butter, at room temperature
2 cups confectioners’ sugar, sifted
4 tbsp. unsweetened Dutch-process cocoa powder
Pinch of salt
2/3 cup plus 1 tbsp. sour cream
To make the cake, preheat the oven to 350˚ F. Butter the edges of 2 9-inch round cake pans and dust with cocoa powder, shaking out the excess. Line the bottoms of the pans with parchment paper. In a medium bowl, combine the cocoa powder, espresso powder, and boiling water. Whisk until smooth; set aside to cool slightly. When cooled down a bit, whisk in the sour cream and vanilla. Set aside. In the bowl of an electric mixer, beat the butter on medium-high speed until smooth, about 1 minute. Gradually blend in the sugar and whip on medium-high speed until light and fluffy, 2-3 minutes more. Blend in the eggs one at a time. In a medium bowl, combine the flour, baking soda, and salt; whisk to blend.
With the mixer on low speed, add the dry ingredients in three additions alternating with the sour cream mixture, beating each addition just until incorporated. Divide the batter evenly between the prepared pans. Bake the cake layers for about 23-27 minutes or until a toothpick inserted in the center comes out clean, rotating the pans during halfway through to ensure even baking. Transfer the baked cake layers to a wire rack and let cool in the pans at least 30 minutes before inverting onto the rack to cool completely.
To make the frosting, melt the chocolate in a heat-proof bowl set over a pot of simmering water. Set aside to cool until just barely warm. In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese and butter on medium-high speed until pale and fluffy, about 3-4 minutes. Gradually mix in the confectioners’ sugar, cocoa powder and salt. Beat in the melted and cooled chocolate and then the sour cream. Continue beating until the mixture is smooth and well blended.
To assemble the cake, place one of the cake layers on a cake board or serving platter. Spread an even layer of the frosting over the top of the cake. Top with the second cake layer. Frost the top and sides of the cake using a thin crumb coat at first. Place in the freezer for 30 minutes to set. (While the crumb coat sets, you may want to leave the mixer on low speed with the remaining frosting so that the melted chocolate doesn’t set. Once the crumb cake is set, frost the top and sides of the cake again using an offset spatula or spoon for a soft, billowy appearance. Slice and serve.