Melt the butter in a medium saucepan over medium heat. Add the flour and cook, stirring with a wooden spoon, until the flour is lightly toasted. (This is an important step, as you have to slowly toast the flour without burning it. This will help you lose the floury taste.)
In a second saucepan, warm up the milk and gradually ladle it into the butter-flour mixture. Bring the sauce to a boil, whisking constantly, then reduce the heat and simmer for about 15 minutes. Season with nutmeg, salt and pepper.
If the sauce is too thick, add a little more milk; if too runny, return to the heat and whisk in a pat of butter mixed with an equal amount of flour. The most important thing is this: Besciamella should not taste floury. If you think your sauce is ready but can taste a hint of "flouriness," then think again and keep on cooking for a few minutes more.