Dark Cocoa Buttermilk Cake With Cocoa Mascarpone Frosting

½ 8-ounce tub mascarpone cheese (4 ounces) or one-half of an 8-ounce package cream cheese, softened ½ cup butter, softened ⅓ cup Dutch-processed unsweetened cocoa powder or unsweetened cocoa powder 2 tablespoon milk 2 teaspoon vanilla 1 16 ounce box powdered sugar, sifted (4-1/4 to 4-1/2 cups)