On a plate, season the chops with salt and pepper and set aside. On another plate put 3 tablespoons of the flour and then dredge the seasoned pork chops in it so they are fully coated.
Heat 2 tablespoons of the butter and oil in a large skillet (12-inch diameter) over high and once hot, sear the floured pork chops, undisturbed, until golden brown, about 5 minutes. Turn over and sear the other side just until the pink meat has browned slightly, about 2 minutes. Turn the heat down to medium-low and transfer the chops back to the plate.
Add the remaining 2 tablespoons butter to the pan and once melted, scrape up all the brown bits. Add the shallots and cook, stirring frequently, until very soft and golden brown, about 5 to 7 minutes. Stir in the remaining 3 tablespoons flour and cook, stirring often, until saturated in the shallot butter and cooked, about 3 minutes. Slowly pour in the chicken broth while whisking vigorously to incorporate it. Bring to a simmer. Stir in the thyme, 1 teaspoon of freshly ground black pepper, nutmeg and cayenne then season with salt.
Place the pork chops in the gravy and simmer until cooked through to your liking or chops registers 135º F with an instant-read thermometer stuck into the thickest part, about 7 minutes. Turn off the heat. Let the chops rest in the gravy and come up to temperature (150º F for medium). Serve on a platter with the chopped parsley and more black pepper on top, if desired.