Melt the butter in a saucepan over low to medium heat. Using a wooden spoon, stir in the flour and mix well. Continuing stirring over low heat for two minutes.
Using a whisk, and continually whisking, add the milk in small quantities - about two tablespoons at a time. Make sure that you fully incorporate the liquid before adding more - this way you will get a smooth sauce.
After you've added about half the milk, pour in the rest and give the mixture a good whisking. Continue to heat the sauce on low to medium heat, whisking often. Cook just to below boiling until the mixture thickens.
Remove from heat and mix in the egg yolk and cream mixture, continually stirring so the egg doesn't cook into a clump.
Stir in the cheese, two tablespoons at a time, fully incorporating it into the sauce. You may need to reheat the sauce briefly on low heat.
Season to tate with nutmeg, salt and pepper.
Makes about 1 1/2 cups sauce.