Melt butter in a large skillet over medium heat. Season pork chops with salt and pepper on both sides, then cook in skillet for about 10 minutes, flipping once, until pork reaches an internal temperature of 160 degrees F. Transfer to a plate and cover with foil.
Whisk flour into milk in a bowl, then pour into the skillet. When milk comes to a boil, simmer for about 2 minutes to thicken. Add cheese, onion, parsley, thyme, and nutmeg. Stir and cook for 1 more minute.
Serve pork chops with Parmesan sauce spooned over each.