In a large frying pan or pot, add butter and melt over low heat.
Once melted, increase heat to medium-high, add flour and whisk through the butter, once gently simmering, cook for 1 minute, while whisking.
Pour milk in a slow steady stream while whisking over medium heat.
Continue to cook and whisk over medium heat until it thickens, do not let it boil or simmer, it will thicken before it reaches a bubble.
Once thickened, reduce heat to low.
Whisk through ground nutmeg, and season with salt and pepper to taste.
Add thawed shredded cheese and whisk until melted over low-medium heat.
Turn off heat and set it aside.