Our classic sheet cake is the tried-and-true foundation for a traditional birthday cake. The cake ingredients are enough to make one layer; you will need two to assemble the cake.
Preheat oven to 350 degrees. Butter a 17-by-12-by-1-inch rimmed sheet pan. Line bottom with parchment, butter parchment, and dust pan with flour, tapping out any excess; set aside.
Sift together the flour, baking powder, and salt into a medium bowl, and set aside. Beat the butter in the bowl of an electric mixture fitted with the paddle attachment until it is creamy. Add the sugar to the butter in a steady stream, and continue beating until the butter is light and fluffy, about 3 minutes. Reduce speed to low, and add dry ingredients alternately with the milk and vanilla in three additions, starting and finishing with the dry ingredients; be careful not to overmix. Set batter aside.
In a medium metal bowl or clean bowl of an electric mixer, whisk egg whites just until stiff peaks form. Fold one-third of the egg whites into the batter until combined. Fold in remaining whites in two batches. Pour batter into prepared pan, and smooth top with a metal spatula. Bake until a tester inserted near the center comes out clean and the cake springs back when pressed lightly in the center, about 30 minutes. Let pan cool 15 minutes on a wire rack before unmolding. Loosen the sides with a small metal spatula or paring knife, and invert onto greased wire rack. To prevent the layer from splitting, invert again so that the top is up. Cool completely before assembling cake or wrapping airtight to freeze cake for later. While this layer cools, repeat steps with a second batch of ingredients for a second cake layer.
To assemble, trim tops of each layer so they are flat. Place one layer of cake on serving platter. Set aside, covered, 1 cup of the icing for coloring. Spread top of cake layer with 1/4-inch layer of the icing, and cover with second cake layer. Frost cake, using remaining icing. Chill cake.
Place chocolate in a heat-proof bowl set over a pan of barely simmering water. Stir, using a plastic spatula, until melted. Remove bowl from heat, and set aside to cool for about 15 minutes, until no longer warm but still liquid. Roll a parchment triangle into a tight cone. Fill halfway with melted chocolate. Roll down the top of the cone like you are rolling a tube of toothpaste. Avoid overfilling, because it will be harder to pipe decorations. Remove cake from refrigerator; using sharp kitchen shears, cut a very small hole in tip of filled cone. Pipe desired decoration with chocolate; set aside for 10 minutes to set. Color remaining cup of icing, if desired; pipe designs on cake.