Combine the brine ingredients in a large bowl and stir until the brown sugar and salt have dissolved. Put the pork into the brine, ensuring it is fully submerged. Leave the pork in the brine for at least 24 hours.
When ready to cook, set Smoker grill temperature to 180℉ and preheat, lid closed for 15 minutes. For optimal flavor, use Super Smoke if available.
Take the pork shoulder out of the brine and set it directly on the grill grate, fat-side up. Allow it to smoke for 3 hours, spraying it with apple juice every hour.
Meanwhile, whisk together the ingredients for the barbacoa sauce in a bowl and set aside.
After smoking the pork shoulder for 3 hours, increase the grill temperature to 250°F and roast for an additional 5 hours, or until an instant-read meat thermometer inserted in the thickest part, but not touching bone, registers 195°F. When it's ready you should be able to give the bone a gentle twist and pull, and the bone should come out with relative ease.
After it reaches 195°F, carefully take the pork off of the Traeger and wrap with foil and a towel. Keep in a cooler or warm oven for 30 minutes to an hour.
Pull the pork into chunks. Discard the bone and any lumps of fat, including the cap. Pull each chunk into shreds, and transfer to a large mixing bowl.
Add in the barbacoa sauce and mix together thoroughly. Serve with sides, such as black beans, cilantro lime rice, avocado and a few sprigs of fresh cilantro. Enjoy!