Place rack in middle of the oven. Heat oven to 300 degrees F. Butter 6 (4 by 2-inch) round cake pans and dust with cocoa powder; tapping out excess. Sift cocoa into a large bowl; whisk in boiling coffee and milk. Let cool. Sift together cake flour, baking soda, and salt in another bowl. Set aside. In a large bowl with a rubber spatula mix the butter until light and fluffy, about 2 minutes. Gradually add sugar and vanilla. Add the eggs 1 at a time, stirring well after each addition. Pour in the cooled cocoa mixture. Mix until fully incorporated. Add the sifted dry ingredients to the chocolate mixture, stirring until just combined. Pour the batter into the prepared pans. Bake for 20 minutes, rotate the pans, and bake about 15 minutes more, (until a cake tester comes out clean when inserted into the center of the cake.) Remove cakes from oven and allow cakes to cool in pans for 15 minutes on a cooling rack. Cut excess cake from top of pans with serrated knife. Carefully run a small offset spatula around the edge of the cakes to loosen them from the pan. Remove cakes from pans and invert onto a wire rack. Let cool completely, about 1 hour. Use about 3/4 cup buttercream to frost each cake. Divide remaining frosting between 4 small bowls; tint each a different color with liquid or gel food coloring. Transfer tinted buttercream to pastry bags fitted with decorative tips. Decorate frosted cakes as desired with tinted buttercream and colored sprinkles.
Combine the egg whites, sugar, and vanilla in the heatproof bowl of an electric mixer. Set the bowl over a pan of simmering water. Whisk constantly until the sugar has dissolved and whites are hot to the touch, 5 to 7 minutes. Transfer the bowl to the electric mixer. Using the whisk attachment, mix on low speed, gradually increasing to high speed, until stiff, glossy peaks form, about 10 minutes. In a separate bowl, beat butter until creamy and fluffy. At low speed, add the butter to the egg whites until smooth. Add the vanilla and continue mixing until incorporated. Yield: 8 cups