Place the onion, cabbage, and apples in the bottom of a slow cooker.
Pat pork dry with paper towels. Season on all sides with salt and pepper, to taste.
Heat vegetable oil in a large skillet over medium-high heat until just smoking. Brown the roast on both sides, 7-10 minutes. Do not wipe out the skillet. Place the pork (fat-side up) on top of the vegetables in the slow cooker.
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. Cook over medium-high heat for about 1 minute, scraping any browned bits from the bottom of the pan with a wooden spoon (these add great flavor to the sauce). Pour the apple cider mixture into the slow cooker.
Cover and cook until the pork registers 140°F and the vegetables are tender, about 3-4 hours on LOW or 1 ½ - 2 hours on HIGH. Season the meat and vegetables with additional salt and pepper, to taste. If the meat isn’t as brown on the outside as you’d like, you can transfer the pork to a rimmed baking sheet and place it under the broiler for a few minutes before slicing and serving.