Melt the butter in a pot over medium heat.
Once the butter is melted, whisk in the flour. Let the mixture simmer for about 2 minutes, stirring constantly, to get a light roux. Make sure it doesn't brown.
Remove the pot briefly from the heat and gradually pour in the cold or slightly warmed milk, whisking constantly. This is important to prevent lumps.
Return the pot to the stove and bring the sauce to a boil, stirring constantly. Then let it simmer gently over low heat for about 10-15 minutes until it thickens and the flour taste is cooked out. Stir frequently to prevent burning.
Season the Béchamel sauce generously with salt, pepper, and a pinch of freshly grated nutmeg.
Enjoy this super delicious Classic Béchamel Sauce. It's the perfect base for many dishes!