Position a rack in the lower third of the oven, place a rimmed baking sheet on the rack and preheat to 450 degrees . In a heavy skillet, heat 1 tablespoon olive oil over medium heat. Add the onion and cook, stirring, until softened, 5 minutes. Stir in the apple, 1/4 cup cider and the caraway seeds; season with salt and pepper. Cook, stirring occasionally, for 5 minutes. Remove from the heat and stir in the granola and parsley.
Holding a paring knife parallel to the work surface, cut a 2-inch-wide pocket through the center of each chop, cutting from the fatty side toward the bone. Spoon a quarter of the stuffing into each pocket. Season the chops with salt and pepper.
In a large, heavy skillet, heat the remaining 3 tablespoons olive oil over medium-high heat until just beginning to smoke. Add the chops, lower the heat and cook, turning once, until browned on each side, about 8 minutes total.
Transfer the chops to the preheated baking sheet and reserve the skillet. Roast the chops, flipping them halfway through cooking, until an instant-read thermometer inserted into the stuffing registers 140 degrees , about 15 minutes. Transfer the chops to a platter, tent loosely with foil and let rest for 10 minutes; reserve the baking sheet.
Meanwhile, discard all but 1 tablespoon oil from the reserved skillet and stir in the flour over low heat for 1 minute. Whisk in 1/2 cup water and the remaining 1 cup cider and bring to a boil, whisking. Lower the heat and simmer, whisking occasionally, until reduced to about 3/4 cup, about 5 minutes. Discard any fat from the baking sheet, then scrape the browned bits and juices into the gravy. Season with salt and pepper and spoon over the pork chops.