In the microwave or on in a saucepan, melt together ½ cup of the butter (1 stick) cocoa and milk and stir until smooth. Cool slightly.
In another large bowl, beat remaining butter and vanilla together, then add cooled cocoa mixture.
Add confectioners' sugar 1 cup at a time, blending with each addition, until frosting is smooth and creamy. For a stiffer frosting for piping, use all 8 cups of sugar. For a softer frosting for swooping on a cake, use just 7 cups of confectioners' sugar.
Melting the cocoa and butter together activates the chocolate flavors in the cocoa. It also helps make the frosting smooth and creamy.
I prefer using unsalted butter in this milk chocolate frosting recipe. Salted butters contain varying amounts of salt and can throw off the flavor of the frosting.
If you'd like to make a stiffer frosting for piping, use all 8 cups of sugar. To make a softer frosting for swooping on a cake, use 7 cups of confectioners' sugar.