Cut the pork shoulder into roughly 2-inch pieces. Pat dry with paper towels.
Mix together the brown sugar, smoked paprika, garlic powder, onion powder, cumin, salt, and pepper. Coat the pork pieces generously with the dry rub.
Preheat the air fryer to 400F. Place the seasoned pork in a single layer in the basket.
Cook at 400F for 15 minutes, then reduce the temperature to 325F and cook for an additional 25 minutes until the internal temperature reaches 200F.
Let the pork rest for 5 minutes, then shred with two forks. Toss with barbecue sauce and serve on buns or however you prefer.