Cook flour and milk on low heat until very, very thick. Cool completely before moving forward with the recipe.
Cream sugar and butter and vanilla until fluffy. Add to completely cooled flour and milk mixture. Using a paddle attachment, mix on high speed with an electric mixer until the mixture is the consistency of whipped cream. Spread the frosting on completely cooled cakes or other desserts.
Store in the refrigerator.
Notes
from Favorite Recipes of Home Economics Teachers, Desserts Edition, 1963Makes about 2 1/2 cups.