¾ cup (180 grams) whole milk, room temperature3 tablespoons (30 grams) hot chocolate cocoa powder*½ cup (120 grams) plus 3 tablespoons (45 grams) coffee liqueur*, divided1 cup (227 grams) unsalted butter, softened2 cups (400 grams) granulated sugar4 large eggs (200 grams), room temperature2 teaspoons (8 grams) vanilla extract2½ cups (313 grams) cake flour½ cup (43 grams) unsweetened cocoa powder1 tablespoon (15 grams) baking powder½ teaspoon (1.5 grams) kosher saltChocolate Meringue Buttercream (recipe follows)4 cups (296 grams) Italian Meringue (recipe follows)
Preheat oven to 350°F (180°C). Spray 2 tall-sided 8-inch round cake pans with baking spray with flour.
In a small saucepan, heat milk over medium heat until steaming. (Do not boil.) Remove from heat, and whisk in hot chocolate powder until completely dissolved. Whisk in 3 tablespoons (45 grams) liqueur. Let cool slightly.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.
In a medium bowl, whisk together flour, unsweetened cocoa, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Divide batter between prepared pans, smoothing tops with an offset spatula.
Bake until a wooden pick inserted in center comes out clean, 28 to 30 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.
Trim cooled cake layers flat, and brush layers with remaining ½ cup (120 grams) liqueur. Place 1 cake layer on a cake plate; spread Chocolate Meringue Buttercream on top, and top with remaining cake layer. Spread Italian Meringue on top and sides of cake. Using a handheld kitchen torch, carefully brown meringue. Store in an airtight container. Best served same day, but finished cake can be refrigerated for up to 2 days.