In a screw-top jar combine 1 cup milk and 1/4 cup flour. Cover and shake well. Place milk mixture in a small saucepan. Cook and stir over medium heat until thickened and bubbly. Reduce heat; cook and stir for 2 minutes more. Remove from heat. Transfer cooked mixture to a small bowl. Cover surface with plastic wrap and refrigerate at least 2 hours or until thoroughly chilled.
In a large mixing bowl beat 1 cup butter, 1 cup sugar, and 1 teaspoon vanilla with an electric mixer on medium speed until light and fluffy and sugar is almost dissolved. Add the chilled cooked mixture, 1/4 at a time, beating on medium speed after each addition until smooth.