In a saucepan, melt the butter at low heat. When fully melted, add the flour and mix with a spoon or a whisk to make a thick paste.
Immediately add the milk and whisk energetically. Turn the heat to medium and bring the milk to a simmer while keep whisking.
When the milk starts to thicken and simmer, turn down the heat and keep whisking gently to make sure there aren't any lumps.
Once the sauce reaches the desidered thickness, turn off the heat and season with salt, a pinch of grated nutmeg and some black pepper to taste.
Notes
Milk: You can use any type of milk to make Béchamel. Since the thickening is caused by the butter and flour, it doesn't really matter how fat is the milk. It may, of course, impact the taste slightly, but feel free to use whichever milk you prefer.TIP: Most recipes tell you to warm the milk in a separate pot. This is though not necessary. You can use room temperature or cold milk and still get a smooth sauce without clumps. The critical step is to whisk well, as soon as you pour the milk until it thickens.