Make chocolate cake according to package directions baking it 20 minutes on a cookie sheet. Cook flour and milk until thick. Cool. Mix sugar, shortening, 1/2 tablespoon butter and 1 teaspoon vanilla until smooth. Add flour mixture and beat well. Spread over cake and refrigerate.
Mix baking chocolate, 1 stick butter, egg, powdered sugar, hot water and 1 tablespoon vanilla. Spread on top of white frosting on cake.