Melt the butter in a medium saucepan over medium-low heat.
Add the flour and whisk continuously for 2 minutes to form a smooth roux. Do not allow it to brown.
Slowly pour in the warm milk while whisking constantly to prevent lumps.
Continue whisking until all the milk has been incorporated.
Simmer gently for 8–10 minutes, stirring frequently, until the sauce thickens and coats the back of a spoon.
Stir in the salt, black pepper, and nutmeg.
Add the Parmesan cheese, if using, and whisk until melted and smooth.
Remove the saucepan from the heat.
Let the Béchamel Sauce rest for 5 minutes before using or serving. Stir once more before adding it to recipes.