Layer the vegetables: Place the onion, cabbage, and apples in the bottom of a slow cooker.
Season the pork: Pat the pork dry with paper towels. Season on all sides with salt and pepper, to taste.
Sear the roast: Heat the vegetable oil in a large skillet over medium-high heat until just smoking. Brown the roast on both sides, 7 to 10 minutes. Do not wipe out the skillet. Place the pork fat side up on top of the vegetables in the slow cooker.
Deglaze the skillet: In a small bowl or large measuring cup, whisk together the apple cider, mustard, vinegar, and brown sugar. Add the liquid to the skillet with the pork drippings and cook over medium-high heat for about 1 minute, scraping any browned bits from the bottom of the pan. Pour the mixture into the slow cooker.
Cook until tender: Cover and cook until the pork registers 140°F and the vegetables are tender, about 3 to 4 hours on LOW or 1½ to 2 hours on HIGH. Season the meat and vegetables with additional salt and pepper, to taste.
Rest and serve: Transfer the pork to a cutting board and rest for 5 to 10 minutes before slicing. For a darker crust, place the roast on a rimmed baking sheet under the broiler for a few minutes before resting.