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.
Add the cheese about 2 tablespoons at a time, thoroughly incorporating each addtion.
Remove from heat and whisk in nutmeg, salt and pepper.