Make the Roux: Melt the butter in a pan on medium-low heat. Add flour and stir continuously for two minutes until it becomes a smooth, yellow paste. Slowly pour in the milk while whisking continuously.
Simmer: Continue to cook while stirring, until the sauce becomes thick and creamy. Add salt, black pepper, and nutmeg to the mixture. Adjust the seasoning according to your taste. Add some more milk to reach the desired consistency if the sauce is too thick and gloopy.