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 250 degrees F and preheat, lid closed, for 10 to 15 minutes.
While Traeger comes to temperature, trim excess fat off pork butt. Generously season with Traeger Big Game Rub on all sides.
Put pork butt directly on the grill grate and cook until the internal temperature reaches 160 degrees F (approximately 3-5 hours). Remove the pork butt from the grill.
On a large baking sheet, stack 4 large pieces of aluminum foil on top of each other, ensuring they are wide enough to wrap the pork butt entirely on all sides. If not, overlap the foil pieces to create a wider base.
Place the pork butt in the center on the foil, then bring up the sides of the foil a little bit before pouring the apple cider on top of the pork butt. Wrap the foil tightly around the pork, ensuring the cider does not escape.
Place the foil-wrapped pork butt back on the grill and cook until the internal temperature reaches 204 degrees F, in the thickest part of the meat, about 3-4 hours longer depending on the size of the pork butt.
Remove from the grill. Allow the pork to rest for 45 minutes in the foil packet. Remove the foil and pour off any excess liquid into a fat separator.
Place the pork in a dish large enough to “pull” the meat, removing and discarding the bone and any excess fat. Add separated liquid back to pork and season to taste with additional Big Game Rub.
Serve alone, in your favorite recipes, or on sandwiches. Refrigerate leftover pork in a covered container for up to 4 days. Enjoy!