In a medium saucepan, melt the butter over medium heat.
Add the flour and whisk until combined and lightly browned, about 1 minute.
Slowly add the milk, whisking constantly to prevent lumps from forming.
Bring the mixture to a simmer and cook for 2 minutes, stirring occasionally.
Reduce the heat to low and add the Gruyere cheese, nutmeg, pepper, and salt. Stir until the cheese is melted and fully incorporated into the sauce.
Serve warm over your favorite dishes or store in an airtight container in the refrigerator for up to 3 days.
