Heat oil in a large frying pan over high heat. Season pork chops with 1/2 tsp. each salt and pepper. Cook, turning once, until browned but still slightly pink in center, 5 minutes total. Transfer to a plate, tent with foil, and let rest.
Melt butter in the same pan. Cook cabbage, bell pepper, onion, apple, and carrots until just starting to soften, about 5 minutes. Mix in vinegar, sugar, and remaining 1/2 tsp. each salt and pepper. Serve with pork chops.
Note: Nutritional analysis is per serving.