How to Make It
Whisk together salt, sugar, paprika, mustard, pepper, garlic powder, cumin, and cayenne in a small bowl. Transfer 1/4 cup of the spice mixture to a separate small bowl, and whisk in apple juice; set aside.
Pat pork shoulder dry, and place on a rimmed baking sheet. Rub remaining dry spice mixture evenly over entire surface of pork, pressing to adhere.
Fill a pellet container to an electric pellet grill with hardwood pellets according to manufacturer’s instructions. Set temperature to 225°F, close lid, and preheat pellet grill 10 to 15 minutes. Place pork, fat cap side up, on grill grate, close lid, and grill, basting with apple juice mixture every hour, until a meat thermometer inserted into thickest portion of pork registers 150°F to 155°F, 5 1/2 to 6 1/2 hours.
Carefully remove pork from pellet grill (it will be hot), and wrap tightly in 2 layers of aluminum foil. Return to grill; close lid, and grill until a meat thermometer inserted in center of pork reaches an internal temperature of 200°F to 205°F, 2 1/2 to 3 1/2 hours.
Transfer to a cutting board, and let rest in foil 1 hour. Remove pork from foil, reserving drippings in foil. Using 2 forks, shred pork into large pieces, discarding bone and fat. Place shredded pork in a large bowl; add drippings, and toss to combine.