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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.