Put the pork chops on a plate and sprinkle both sides with the salt and a generous shower of black pepper.
Put a cast iron or other large heavy skillet on the stove over medium-high heat. Leave it to get very hot, 2 to 3 minutes. Add the oil and tilt the pan so it coats the bottom and gets hot. Lay down the chops and cook until nicely browned on the first side, about 4 minutes. Turn them over and cook until an instant read thermometer measures 140 degrees in the thickest part, another 2 to 3 minutes. The time will vary depending on the size of the chops. If you don't have an instant read thermometer, cook them until the meat is just a hint pink when you cut into the center.
While the chops brown, in a small bowl stir together the mustard, maple syrup, sour cream, and vinegar. Set aside.
Transfer the cooked chops to a plate to rest. Add the sliced apple to the pan and sauté until golden and a little tender, a few minutes more. Return the chops to the pan. Spoon a little sauce over each chop and serve immediately.