In a small saucepan mix the flour and the milk and cook over low heat until it forms a smooth paste with no lumps. Place in refrigerator and let cool completely.
With an electric mixer beat the shortening, butter or margarine and the sugar until light and fluffy. Beat in the cooled flour paste and mix until smooth. Stir in the vanilla. Use to frost any cooled cake. Makes enough to frost one 9x13 inch sheet cake or two 8 or 9 inch layer cakes.