Preheat the oven to 400°F. Season the pork chops on both sides with salt and pepper. Heat half of the oil in a large skillet over high heat until shimmering. Add the pork chops and cook over moderate heat until golden, turning once, 8 minutes. Transfer the meat to a baking sheet and roast in the oven until cooked through, about 10 minutes.
Meanwhile, check the amount of fat left in the skillet; if there isn't at least a tablespoon, add the remaining oil as needed. Heat the oil and fat until shimmering. Add the shallot and cook over moderately high heat until softened, 3 minutes. Add the vinegar and cook until nearly evaporated, about 30 seconds. Add the stock and cook until reduced by half, about 2 minutes. Add the cream and cook over moderately high heat until slightly reduced, about 2 minutes. Stir in the mustard and parsley. Season with salt and pepper. Transfer the pork to plates and spoon the sauce on top.
