In a medium saucepan placed over medium heat, melt  butter. Add  flour and cook, whisking constantly, until the flour turns light brown and emits a nutty aroma.

Slowly add the milk, whisking constantly. When the milk has been incorporated, whisk in the nutmeg, and allow the mixture to come to a simmer. Simmer 2 minutes, whisking constantly.

Remove from heat, and add shredded Provolone a handful at a time, stirring until it melts. Stir in Parmesan cheese and season with salt and pepper.