Trim any excess fat from the pork shoulder. Rub the meat evenly with smoked paprika, cumin, garlic powder, salt, and black pepper.
Place the seasoned pork in the slow cooker and pour the chicken broth around it. Cover and cook on low for 8 hours until the pork pulls apart easily with a fork.
While the pork cooks, prepare the slaw. In a mixing bowl, combine the sliced apples, shredded cabbage, and shredded carrot.
In a small bowl, whisk together the apple cider vinegar, mayonnaise, and honey. Pour the dressing over the slaw and toss until evenly coated. Set aside in the refrigerator.
Once the pork is done, shred it directly in the slow cooker using two forks. Stir the shredded meat into the juices to keep it moist.
Serve the pulled pork topped with the tangy apple slaw.