Melt 3 tablespoons of the butter in a medium saucepan over medium heat.
Whisk in the flour until smooth.
Cook, stirring, for 1 minute.
Add the milk, 1 1/2 teaspoons salt, and nutmeg and bring to a boil while whisking constantly.
Lower the heat and simmer, stirring occasionally, until the white sauce is thickened, about 10 minutes.
Season with pepper. Remove from the heat.