Pat the pork shoulder dry with paper towels.
Combine the dry-rub ingredients in a small bowl.
Coat the pork with mustard, then generously apply the dry rub.
Place onion and garlic in the slow cooker or roasting pan.
Combine BBQ sauce, Worcestershire sauce, apple cider vinegar or apple juice, and broth.
Place the pork over the onion mixture and add the cooking liquid.
For the slow cooker, cook on LOW for 8–10 hours or HIGH for approximately 5–6 hours.
For the oven, cover tightly and cook at 300°F (150°C) for approximately 4–5 hours.
Check the pork for tenderness. It should pull apart easily with a fork.
Rest the pork for 15–20 minutes.
Shred the pork using two forks.
Mix with the cooking juices and additional BBQ sauce.
For crispy edges, spread the shredded pork onto a baking sheet and roast briefly at high heat.
Serve hot on buns or with your favorite barbecue sides.