In a small saucepan over medium heat, melt the butter. Gradually add the flour, stirring constantly, and cook until it is lightly golden or toasted. Stir often to prevent burning. (This is your roux.)

Mix the milk with the salt and nutmeg. Slowly pour in the milk while whisking constantly to avoid lumps. Let the sauce cook and thicken slowly. Continue stirring so it doesn't stick or burn on the bottom. Once it comes to a boil, reduce the heat to low and cook for about 15 more minutes, stirring occasionally. If you want a thinner sauce, add a little more milk.