Preheat the oven to 400°. Season the pork chops on both sides with salt and pepper. In a large skillet, heat half of the oil 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 until cooked through, about 10 minutes.
Meanwhile, pour off the fat from the skillet. Add the remaining oil and heat until shimmering. Add the shallot and cook over moderately high heat until softened, 3 minutes. Add the vinegar and cook until nearly evaporated, about 1/2 minute. 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. Add the mustard and parsley. Season with salt and pepper. Transfer the pork to plates and spoon the sauce on top.