Preheat oven to 325°. Sift together dry ingredients in a bowl. Add oil, coffee, and milk; mix at medium speed 1 minute. Add eggs and vanilla; beat 2 minutes longer. (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 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.