Season both sides of the pork chops with salt and pepper. In a large skillet, heat the oil over medium-high heat until it shimmers. Add the pork chops, reduce the heat to medium, and cook, turning once, until slightly pink inside (145ºF), 6 to 8 minutes. Transfer the pork chops to a platter and cover with foil to keep warm.
Drain off all but a sheen of fat from the skillet. Add the shallot to the pan and sauté briefly, until translucent. Add the broth and the wine to the skillet, stirring with a whisk to loosen any browned bits from the bottom of the pan. Bring to a boil and boil until the liquid is reduced to 1/2 cup, cooking about 4 to 5 minutes, depending on the heat and your pan size. Whisk in the mustard and butter. Bring to a boil and whisk in the cream and the parsley.
Divide the chops among four dinner plates, spoon the sauce over the chops, and serve.
Pork Chops with Cornichon-Mustard Sauce: Stir 1/4 cup julienned cornichons into the finished sauce and gently heat through.
Pork Chops with Mustard-Caper Sauce: Add 1/4 teaspoon crushed dried herbes de Provence when you add the shallot. Stir 1/4 cup drained capers into the finished sauce.