Trim pork butt of all excess fat leaving 1/4-inch of the fat cap attached.
Combine 2 Tbsp Traeger Pork & Poultry Rub, apple juice, brown sugar and salt in a small bowl stirring until most of the sugar and salt are dissolved.
Inject the pork butt every square inch or so with the apple juice mixture. Season the exterior of the pork butt with remaining rub.
When ready to cook, start the Traeger grill according to grill instructions. Set the temperature to 250 degrees F and preheat, lid closed, for 10 to 15 minutes.
Place pork butt directly on the grill grate and cook for about 6 hours or until the internal temperature reaches 160 degrees F. Remove pork butt from grill and wrap in two layers of foil. Pour in 1/2 cup of apple juice. Secure tin foil tightly to contain the apple juice.
Increase temperature to 275 degrees F and return to grill in a pan large enough to hold the pork butt in case of leaks. Cook an additional 3 hours or until internal temperature reaches 205 degrees F.
Remove from the grill and discard the bone. Shred the pork removing any excess fat or tendons. Season with additional Traeger Pork & Poultry Rub and salt if needed. Add Traeger Sweet & Heat BBQ Sauce and mix to combine. Set pork aside.
For the grilled cheese sandwiches: Butter two pieces of bread and place one in a pan warmed over medium heat, butter side down. Place a slice of cheddar cheese on top of the bread and top with pulled pork. Place another slice of cheese on top of pork and finish with the other slice of bread, butter side up.
Cook on first side 5-7 minutes until bread is lightly browned. Flip and cook for another 5-7 minutes. Remove from heat and slice in half. Enjoy!
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