Preheat oven to 350 degrees F (175 degrees C). Grease three 9-inch round baking pans.
Combine 8 ounces baking chocolate and 2 tablespoons cream in a saucepan over low heat; cook and stir until chocolate is melted, about 5 minutes. Set aside to cool.
Beat 1 cup butter, white sugar, and brown sugar together in a bowl using an electric mixer until creamy; mix in sour cream, 1 cup coffee, eggs, and vanilla extract. Slowly beat in melted chocolate mixture until combined.
Mix flour, baking soda, baking powder, and salt together in a bowl; beat flour mixture into butter mixture until well combined and smooth. Pour batter into the 3 prepared baking pans.
Bake in the preheated oven until a toothpick inserted in the center of a cake comes out clean, 20 to 30 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
Heat 1/2 cup cream and 4 ounces baking chocolate together in a saucepan over medium heat, stirring constantly, until chocolate is melted, about 5 minutes. Remove saucepan from heat and stir in 1/3 cup coffee. Refrigerate mixture until completely cooled, about 30 minutes.
Beat confectioners' sugar and 1 cup butter into cooled chocolate mixture in a large bowl until fluffy; add more confectioners' sugar until desired consistency is reached.
Place 1 cake on a serving platter; spread icing on top of cake. Repeat layering with remaining cake and icing; spread icing on top and sides of entire layered cake.