Pat the pork shoulder dry with paper towels. In a small bowl, mix the brown sugar, smoked paprika, garlic powder, onion powder, salt, black pepper, cayenne pepper, and mustard powder. Rub this mixture generously all over the pork, pressing it into the meat for maximum flavor.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Sear the pork on all sides until golden brown (about 2-3 minutes per side). This step adds a deeper flavor but can be skipped if in a hurry.
Place the pork in a slow cooker (crockpot). Pour in chicken broth, apple cider vinegar, Worcestershire sauce, and liquid smoke (if using). Cover and cook on LOW for 8-10 hours or HIGH for 5-6 hours until the pork is fall-apart tender.
Once the pork is done, remove it from the slow cooker and place it on a cutting board. Use two forks to shred the meat, discarding any excess fat.
For saucy pulled pork, return the shredded meat to the slow cooker and mix it with the cooking juices. Add BBQ sauce, honey, apple cider vinegar, and smoked paprika. Let it cook on LOW for another 30 minutes to soak in the flavors.
Serve the pulled pork on toasted buns, in tacos, over rice, or with coleslaw and cornbread for a complete meal.