Melt the butter in pan over medium heat. Whisk in the flour. Pour in all the milk, whisking constantly until it starts to boil.
Season with salt, lower heat, cover and simmer gently, stirring occasionally, for at least 20 minutes. Bechamel sauce should not taste floury. Remove pan from the heat. Taste and add more salt if necessary and season with pepper and nutmeg.
If sauce is too thick, add a little more milk. If it's too thin, return to heat add a pat of butter mixed with equal quantity of flour. For a richer sauce, replace half the milk with same amount of heavy cream; for lighter sauce, add half milk and half water.