Heat the oven to 350ºF. Grease and flour two 9 inch round baking pans.
In a large bowl, whisk together sugar, flour, cocoa powder, baking powder, baking soda, and salt. Add eggs, milk, oil, and vanilla and mix with an electric beater on medium speed for 2 minutes. Stir in boiling water. Pour the batter into the prepared pans.
Bake 30 to 35 minutes or until a wooden toothpick inserted in the center of one of the cakes comes out clean. Let cool 10 minutes, then carefully invert onto a wire rack to cool completely.
To make the frosting, melt the butter and place in a large bowl. Stir in cocoa powder. Alternately add powdered sugar and milk, beating with an electric mixer, until desired consistency is reached. I prefer my frosting a little stiff. If you want a silkier frosting add more milk a little at a time. If you want a stiffer or sweeter frosting, add more powdered sugar.
Use frosting immediately on cooled cakes. Cake will last tightly wrapped in the refrigerator for up to three days.