In a small bowl, combine the smoked paprika, brown sugar, garlic powder, onion powder, salt, and pepper to create a dry rub.
Rub the spice mixture over all sides of the pork shoulder.
Place the seasoned pork into a 6-quart slow cooker.
Pour the chicken broth (or apple juice) around the base of the pork.
Cover and cook on the LOW setting for 8 to 10 hours (or HIGH for 5 to 6 hours) until the meat is fork-tender.
Remove the pork from the slow cooker and transfer to a large bowl or cutting board.
Shred the meat using two forks, removing any large pieces of fat.
Drain the excess liquid from the slow cooker, leaving about 1/4 cup.
Return the shredded pork to the pot and stir in the BBQ sauce and apple cider vinegar.
Toss to coat evenly and cook on LOW for another 20 minutes to let the flavors meld.