In a small mixing bowl, combine paprika, salt, black pepper and cayenne to form the pork rub.
Coat pork shoulder with seasonings and cover with plastic wrap. Refrigerate for 8 to 24 hours.
Preheat grill to medium heat. Place pork shoulder on grill and smoke shoulder using hickory chips. Make sure wood chips are soaked and drained before using. Add charcoal and wood chips as necessary to keep temperature at medium, or between 93 – 107°C.
Smoke pork shoulder for 5-6 hours or until internal temperatures reach 85°C. Apply baste every 20 minutes during the last few hours of cooking. Remember to boil any remaining basting sauce before using it on shredded pork.
Place pork on a large plate and pull apart allowing pork to cool for 5 minutes. Place pulled pork on a bun topped with coleslaw and serve immediately.