In a small bowl, mix together the brown sugar, paprika, garlic powder, onion powder, salt, and black pepper to create a rub.
Evenly coat the pork butt with the rub, pressing it into the meat to ensure full coverage.
Place the seasoned pork butt in a casserole dish and pour the cider over it.
Cover the dish with foil and cook in a preheated oven at 225°F (110°C) for 4-5 hours, or until the pork is tender and easily shreds with a fork.
Remove the pork from the casserole and shred it using two forks. Skim any excess fat from the sauce in the casserole.
Mix the smoky BBQ sauce into the sauce remaining in the casserole and return the shredded pork to the dish, tossing it well to coat it in the sauce.
Cover the dish again and let the pulled pork sit for an additional 15-30 minutes to allow the flavors to meld.
Serve the pulled pork on soft rolls, topped with coleslaw for added crunch and freshness. Enjoy!