Preheat oven to 350°. Heat oil in heavy-bottomed braising pan with tight-fitting lid. Season pork on all sides with salt and pepper. Sear pork in hot oil until browned; transfer to bowl or pan large enough to catch all juices and set aside.
Leave 2 T pork fat/oil in pan and add bacon and onions, cooking until lightly browned. Add garlic, apples, thyme, bay leaves and mustard, then cook 1 min. Deglaze with vinegar and cider, bringing to a simmer. Add pork with all juices. Cut cabbage head into 8 wedges and add to pan evenly around pork.
Cover tightly and place in oven. Braise pork for 1½ to 2 hours until fall-apart tender, turning pork and cabbage halfway through. Taste for salt, pepper and vinegar and adjust, as desired.
Remove pork, cabbage and apples to a platter and reduce pan liquid over medium-high heat just until thickened slightly; pour over pork. Serve alongside potatoes or spätzle.