In a small bowl, stir together the smoked paprika, brown sugar, garlic powder, onion powder, salt, and black pepper.
Rub the spice mixture evenly over all sides of the pork shoulder.
Place the seasoned pork in the slow cooker. Pour the apple cider vinegar and chicken broth around the meat.
Cover and cook on low for 8 hours until the pork pulls apart easily with a fork.
Remove the pork from the slow cooker and shred it with two forks. Return the shredded meat to the slow cooker and stir it into the juices.
In a large bowl, combine the shredded cabbage and carrots. Add the mayonnaise, apple cider vinegar, sugar, and salt. Toss until the vegetables are evenly coated.
Serve the pulled pork with a generous scoop of coleslaw on top or on the side.