Sift together dry ingredients in a bowl. Add oil, coffee and milk; mix at medium speed for 1 minutes. Add eggs and vanilla; beat 2 more minutes. (Batter will be thin.)
Pour into two greased and floured 9-in. round baking pans (or two 8-in. round baking pans and six muffin cups).
Bake at 325° for 25-30 minutes. Cool cakes for 10 minutes before removing from pans. Cool on wire racks.
Meanwhile, for icing,
1 cup milk
5 tablespoons flour
1/2 cup butter, softened
1/2 cup shortening
1 cup sugar
1 teaspoon vanilla extract
combine the milk and flour in a saucepan; cook until thick. Cover and refrigerate.
In a bowl, beat butter, shortening, sugar and vanilla until creamy. Add chilled milk/flour mixture and beat for 10 minutes. Frost cooled cake. Yield: 12 servings.