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"x1 1/2" cake pans. Bake at 325 for 25-30 minutes. Cool cakes 15 minutes before removing from pans. Cool on wire racks. Meanwhile, for icing, combine milk and flour in saucepan; cook until thick. Cover and refrigerate. In a mixing bowl, beat butter, shortening, sugar and vanilla until creamy. Add chilled milk/flour mixture and beat for 10 minutes. Frost cooled cake.