In a medium saucepan, melt the butter over medium heat.
Whisk in the flour and cook for 2 minutes, stirring constantly, to make a roux.
Gradually whisk in the milk and bring to a simmer, continuing to whisk constantly.
Reduce the heat to low and simmer, stirring occasionally, until thickened to your desired consistency, about 10 minutes.
Remove from heat and stir in the nutmeg. Season with salt and pepper to taste.
