Melt the butter in a small pot over medium heat.
Add the flour and stir constantly until you get a golden mixture that bubbles. Take care so that it doesn't get brown (about 2 minutes).
Add the milk gradually while stirring vigorously with the whisk. If you don't do that the sauce will curdle. If you are not comfortable with that, you can add the milk after you warm it but if you stir vigorously it isn't necessary.
Continue stirring. Gradually, the béchamel sauce will start to thicken. Add salt, pepper and nutmeg (if you like), lower the heat even more and whisk for a while longer.
