Sift together sugar and flour in a large bowl; set aside.
Combine butter and next 3 ingredients in a medium saucepan over medium-high heat. Bring to a boil, stirring constantly, until butter and shortening melt. Remove from heat, and pour over sugar mixture, stirring until dissolved. Cool slightly.
Stir in buttermilk and next 3 ingredients. Pour into a greased and lightly floured 15- x 10-inch jellyroll pan.
Bake at 400° for 20 minutes. (Cake will have a fudgelike texture.) Spread warm cake with Chocolate Icing.