In a medium saucepan, melt the butter over medium heat. Add the flour and whisk until smooth, about 2 minutes. Gradually add the warm milk, whisking constantly, until the sauce is thick, smooth, and creamy, about 10 minutes (do not allow the béchamel sauce to boil). Remove from the heat and stir in the salt, pepper and nutmeg.
(The sauce can be made up to 3 days ahead. Cool, then cover and refrigerate.)