Begin by heating your milk until it's warm but not boiling. You can do this in the microwave or in a small saucepan on the stovetop. Warming the milk first is crucial because using cold milk can cause the sauce to clump.

In a medium saucepan over low heat, melt the butter completely. Once the butter has melted, add the flour and stir continuously for 1-2 minutes until the mixture turns a light sand color. Don't let it get too dark or it will affect the color and flavor of your sauce.

Increase the heat to medium and slowly pour in the warmed milk while stirring continuously. This gradual addition helps prevent lumps from forming. Continue stirring constantly as you bring the mixture to a boil.

Once the sauce comes to a boil, keep stirring often as it thickens, which should take about 10-15 minutes. When the sauce coats the back of a spoon and doesn't immediately drip off, it's ready. Stir in the salt, pepper, and nutmeg (if using), then taste and adjust the seasonings as needed.

If making a cheesy béchamel, stir in the shredded white cheddar cheese after the sauce has thickened and the seasonings have been added. Remove from heat once the cheese is fully melted and smooth.