Preheat oven to 325°. Sift together dry ingredients in a mixing bowl. Add oil, coffee and milk, mix at medium speed for 2 minutes. Add eggs and vanilla; beat 2 more minutes (batter will be thin) Pour into 2 greased and floured 9-in. round baking pans (or two 8-in. round baking pans and 6 muffin cups).
Bake until a toothpick inserted in the center comes out clean, 25-30 minutes. Cool 10 minutes before removing from pans. Cool on wire racks.
Meanwhile, for icing, combine 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 mixture and beat 10 minutes. Frost cooled cake. If desired, dust with additional cocoa.