Peel the pears. Set them upright on their base and cut in 1/2-inch slices down through the length of the pear toward their base. Remove any seeds from the slices; you should have about 8 slices 1/2 inch thick. Sprinkle the pork chops with the cumin and season well with salt and pepper.
Heat the oil in a large skillet over medium-high heat. When it’s very hot, add the pork chops and sauté, moving them only to flip, until the pork is firm to the touch but still slightly springy, about 3 minutes per side. Transfer the pork to a plate and tent with foil. Discard the oil, add the butter to the pan, and, when it’s foamy, add the pears. Flipping them once, cook the pears until both sides have a brown, caramelized exterior, about 3 minutes total. Transfer the pears to a plate.
Pour the cider and cider vinegar into the pan, scraping to remove any browned bits from the bottom. Simmer the cider mixture until it’s reduced by half. Season the sauce with salt and pepper to taste.
Divide the pear slices onto four plates, layer the pork chops on top, and spoon the sauce over it. Serve immediately.