In a saucepan over medium-low heat, melt the butter.
With a whisk, mix in the flour once the butter is melted and mix until smooth.
Whisk for about 2 minutes, being careful not to burn the butter/flour mixture and until it turns a golden color.
Pour in all the milk, whisking the whole time. Continue to whisk until the mixture thickens (about 2 more minutes) and is completely smooth.
Increase heat to medium and continue to stir as the sauce thickens. The finished result should be the thickness and consistency of gravy. Add in salt and pepper to taste (and nutmeg, if desired).
Use on whatever dish you desire or you can pour it into a container and it will keep in the fridge for up to 5 days.
Notes
If you want to turn this into a cheese sauce, you can add half cup of shredded sharp cheddar cheese during the last 2 minutes of cooking. Makes about 1 cup of sauce.