Preheat oven to 350 degrees. Grease and flour one 9x13-inch pan or two 9-inch cake pans; set aside.
CAKE: In a large mixing bowl, whisk together flour, sugar, cocoa, baking soda, baking powder, and salt. Add eggs, coffee, buttermilk, oil, and vanilla. Beat at medium speed for two minutes. The batter will be thin. Pour batter into prepared pan(s). Bake 35-40 minutes for one 9x13-inch pan, or 30-35 minutes for two 9-inch cake pans. Cool completely.
CHOCOLATE FROSTING: Combine butter and chocolate together with a hand or stand mixer. Gradually add confectioners' sugar, milk, and vanilla. Beat until light and fluffy. Spread frosting on cooled cake(s).
COOK'S NOTE: I like to refrigerate my cake, but it's not necessary.