Mix flour and milk together with a whisk in a med. sauce pan and cook until thick. Cover and cool in fridge for 2 hour.
While waiting for mixture to cool, remove butter from fridge and place in large mixer bowl to get soft, and then whip butter. Add sugar until blended.
Remove cold sauce from fridge. Slowly add sauce one scoop at a time while mixing on med. speed until its all used up and mixed well. Turn mixer on high and mix it until it looks like whipped cream. Frost cakes and put in fridge.