Dissolve flour in cold milk. Set aside.
Melt the butter in a saucepan over low heat. Add the dissolved flour into the melted butter. Stir constantly until mixed and all the lumps are gone, about 2 minutes. Add salt and pepper to taste. Continue cooking over low heat until sauce begins to thicken, stirring constantly.
Note: For a richer sauce, add a few tablespoons of heavy cream. For a thin sauce, add more milk.