In a medium saucepan, melt butter over medium heat. Whisk in flour and cook, stirring constantly, for 2–3 minutes until it smells slightly nutty and turns golden.
Gradually whisk hot milk into the roux, ½ cup at a time, fully combining before each addition. Keep whisking until the sauce is smooth and begins to thicken (about 10 minutes).
Drop the heat to low. Stir in the nutmeg, salt, and pepper. Slowly stir in the cheeses until melted and smooth.
Notes
Whisk constantly to keep lumps out.Warm the milk before adding to help eliminate clumping.Want a richer sauce?
Whisk in one egg yolk after lowering the heat and before adding the cheese
Use half a half cup of heavy cream and half a cup of whole milk instead of one cup whole milk
Mornay sauce will set as it cools. To thin out, add a little milk.