If not already divided, cut the pork shoulder into pieces that are 6” wide. Trim off any excess fat on the outside of the pork. (The meat itself is well-marbled.) Sprinkle the meat with 1 tablespoon of Kosher salt. Place the pork in a Dutch oven or stock pot that has a tight-fitting lid.
Combine the orange juice, lime juice, spice blend, and the garlic cloves. Stir to combine, then pour it over the pork, turning it with tongs to make sure the pork is covered in the marinade. Add up to 1 cup of stock to ensure the marinade is half way up the sides of the pot. Allow the pork to marinate for at least one hour at room temp, turning once. If time permits, allow it to marinate overnight in the fridge.
When ready to cook, preheat the oven or Traeger to 350 degrees F. If the pork has been marinating in the fridge, allow the pot to sit out for one hour before cooking so it can come to room temperature. Place a tight-fitting lid on the pot and cook for 2.5-3.5 hours, or until a fork can easily pierce the meat to shred it.
To remove the excess fat, allow the pork to cool in the pan with the lid off for about an hour. The fat will rise to the top. Use a spoon or ladle to remove the fat from the top. When cool enough to handle, remove the meat from the pan and shred with your hands, discarding any extra pieces of fat as you go.
Taste, adding more salt to the pork if necessary. The pork can be served immediately or placed in a container along with its juices and refrigerated for up to 3 days.
Serve with pickled onions and lime slices along with tortillas for tacos or rice and beans for a family-style meal.