Rub the pork shoulder all over with smoked paprika, cumin, garlic powder, salt, and black pepper. Place it in the slow cooker.
Pour the barbecue sauce and chicken broth over the seasoned pork. Cover and cook on low for 8 hours until the meat is very tender.
While the pork cooks, make the slaw. In a large bowl combine shredded cabbage, shredded carrot, apple cider vinegar, honey, and Dijon mustard. Toss well and refrigerate until serving.
When the pork is done, remove it from the slow cooker and shred it using two forks. Return the shredded meat to the slow cooker and stir to coat it evenly with the sauce.
Serve the pulled pork topped with a scoop of the tangy slaw.