Pork chops cut from the shoulder have more connective tissues that break down as they cook, making them a great choice for a low and slow cook. Browning the bacon and pork chops in a pan first gives this dish layers of added flavor.
Place cabbage, onions, allspice, and thyme in a 5- to 6-quart slow cooker. Season with salt and pepper and toss.
In a large skillet over medium-high heat, cook bacon until it begins to brown and crisp up, about 5 minutes. Transfer bacon and any rendered fat to slow cooker.
Season pork chops with salt and pepper. Swirl oil and butter into pan over high heat. Working in two batches if necessary, cook chops, turning once and pressing down with tongs to make contact with pan, until deep golden brown, 8 to 10 minutes. Transfer to slow cooker, tucking chops into the cabbage.
Add chicken broth and vinegar to pan, scraping up any brown bits with a spoon. Pour sauce over pork chops. Cover and cook on low until pull-apart tender, about 3 hours. Serve with applesauce, sour cream, and a sprinkling of fresh herbs.