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Plan ahead, this recipe brines overnight and cooks all day, but it's well worth the time for these delicious flavors.
In a large bowl, combine all of the brine ingredients and stir until the salt and sugar crystals have completely dissolved. Pour over the pork butt in a food-safe bucket or food storage container. Be sure the pork is almost fully immersed in the brine.
Cover and refrigerate overnight.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 225F and preheat, lid closed, for 10 to 15 minutes.
While the grill preheats, remove the pork butt from the brine and reserve the liquid. Using a meat injector, inject the pork with some of the remaining brine about every two inches across the entire roast. Pour the rest of the brine into a bowl and set aside. This will be used as your mop sauce during the cooking process.
Generously season the roast on all sides with the Traeger Pork & Poultry Rub.
Put the roast on the grill grate, fat-side up, and smoke for 3 hours, mopping with the apple juice brine every hour after the first hour.
Transfer to a disposable aluminum foil pan large enough to hold the roast. Increase the tempera-ture to 250F, and roast for 6 to 8 additional hours, or until an instant-read meat thermometer in-serted in the thickest part, but not touching bone, registers 190-195F. If the pork starts to brown too much, cover it loosely with aluminum foil.
Carefully transfer the pork roast to a cutting board and let it rest for at least 20 minutes. Pour the juices from the bottom of the pan into a gravy separator.
With your hands (preferably protected from the heat with lined, heavy-duty rubber gloves), pull the pork into chunks.
Discard the bone and any lumps of fat, including the cap. Pull each chunk into shreds, and trans-fer to a large mixing bowl.
Season with additional rub and moisten with the reserved pork juice. (Discard any fat that has floated to the top.)
Add barbecue sauce, if desired, and mix well, or serve the barbecue sauce on the side. Pile the pork mixture on the hamburger buns, serve with coleslaw. Enjoy.