Melt the butter over medium heat in a small saucepan.
25 g butter
Add the flour.
25 g flour
Whisk constantly until the flour is fully combined with the butter and forms a white roux.
Cook the roux for 3 to 4 minutes, stirring, without letting it brown: this cooks out the raw flour taste.
Sauce
First, pour in 2 tablespoons of the cold milk.
25 cl milk,
Whisk until the roux has completely absorbed this milk.
Then pour in the rest of the milk a little at a time, whisking constantly: this is what prevents lumps.
Cook over medium heat for about 5 to 7 minutes, stirring constantly so the sauce doesn't stick to the bottom, until it thickens and becomes smooth, glossy and thick enough to coat the back of a spoon.
Adjust the consistency if needed: if it's too thin, cook it a little longer, stirring; if it's too thick, add a little cold milk, a bit at a time, whisking.
Season with the salt, pepper and nutmeg.
Salt, Pepper, 1 pinch nutmeg,
If you're not using the sauce right away, press plastic wrap directly onto its surface to keep a skin from forming.
Notes
A roux is a mixture of equal parts butter and flour. The milk should be cold: it heats up gently and blends in more easily. A good béchamel stays creamy and supple, with enough body to hold together without turning gluey. If lumps form anyway, strain the sauce through a sieve.Storage: 3 to 4 days in the refrigerator, in an airtight container, with plastic wrap pressed directly onto the surface. Béchamel freezes for 2 to 3 months in a freezer-safe container; let it thaw slowly in the refrigerator. To reheat it, warm it over low heat, stirring regularly, and thin it with a little cold milk if it's too thick.Tip: to coat vegetables (asparagus, broccoli, leeks), replace some of the milk with a little of their cooking water.Mornay variation, for gratins: stir 100 g of grated cheese (Gruyère or Comté) into the hot béchamel and let it melt over low heat.These quantities make a small saucepan's worth of sauce (for croque-monsieur or vegetables). For lasagna or a large gratin, double or triple all the quantities.