Preheat the oven to 350°Fahrenheit.
Lightly grease and flour two 9-inch round baking pans.
Sift together the sugar, flour, cocoa, baking powder, baking soda and salt in a large bowl.
Add eggs, milk, oil and vanilla. Beat with an electric mixer, set to medium speed, for 2 minutes. Stir in coffee (batter will be thin). Divide batter evenly between prepared pans.
Bake for 30 to 35 minutes or until wooden pick inserted in center comes out clean. Cool in pans for 10 minutes. Remove cakes from pans to a rack; cool completely.
Stir cocoa powder with butter until well combined. Alternately add sugar and milk, beat to a spreadable consistency. If necessary, add a bit of milk to reach desired consistency; stir in vanilla. Frost between the cake layers, top and sides. Makes 10 to 12 servings. Enjoy!