In a large saucepan, combine the apples, onion, raisins, ginger, brown sugar, vinegar, 3 Tbs. of the butter, the cayenne, and 1/2 tsp. salt. Bring to a boil over high heat. Reduce the heat to maintain a lively simmer and cook until the solids are very tender and the liquid has reduced to a juicy, syrupy glaze, 20 to 25 minutes.
Meanwhile, once the chutney has been simmering for about 15 minutes, season the pork chops with salt and pepper. In a 12-inch skillet, heat the remaining 1 Tbs. butter with the oil over medium-high heat until the butter foams and just begins to turn a nutty brown. Add the pork chops and cook until the first side is deeply browned, 3 to 5 minutes. Flip the chops and continue cooking until the second side is well browned and the chops are cooked through, 3 to 5 minutes.
Stir the cilantro into the chutney and season to taste with salt. Serve the chops topped with the chutney.