In a pot on medium heat, add Butter, allow Butter to melt. Sauté Butter 2 minutes, (until frothing slows down), stirring constantly. Add the Flour, mix in with a spatula , sauté the Flour for a 4 minutes, stirring constantly.

Add Milk, in small batches, stirring continuously so that no lumps form in the mixture. The mixture will be quite thick at first. You need to be persistent and patient. As you add more and more of the Milk, you will see how the Béchamel Sauce will start to become nice and creamy.

To temper the Eggs, slowly add Béchamel Sauce to the Egg Yolks, while mixing continuously.

When ready, remove from heat and add Salt, Pepper, Nutmeg and all of the Cheese.

Set aside until needed.