Preheat oven to 375F. In a large, heavy skillet melt butter and heat olive oil over high heat. Season pork chops with salt and pepper on both sides, sear in skillet until golden brown and flip. When both sides are seared, transfer skillet to preheated oven to finish cooking, about 8-10 more minutes depending on thickness and desired temperature. When done remove skillet from oven and remove chops with tongs to a plate. Tent with foil to retain heat.
Spoon out any fat from skillet in excess of 2 tablespoons. Return skillet to medium-high heat and add shallots. Saute until soft and fragrant. Pour in wine and scrape up any browned bits from bottom of pan with a wooden spoon. Let wine evaporate until almost gone and then stir in apple jelly and chicken stock. The sauce will thicken slightly. Season sauce with salt and pepper. Pour sauce over chops and serve immediately.