Let the meat rest at room temperature for about an hour so it's not going into the smoker too cold.
Preheat your Traeger pellet grill to 225-F as per the manufacturer's instructions.
Rub the pork shoulder all over with the mustard.
Mix the brown sugar, paprika, chili powder, garlic and onion powder, cayenne, salt and pepper in a small bowl.
Rub the pork all over with the dry rub. Make sure it's an even layer on all sides.
Put the pork into a foil pan and smoke it at 225-F for about 4-5 hours, or until the temperature reaches 160-F. Spritz the top and sides of the pork with apple juice every hour.
When the pork reaches 160-F, lift the pork into a clean foil pan or drain the liquid out of the pan. Wrap the pan tightly in foil and continue to smoke for another 5-6 hours or until the internal temperature reaches 200-205-F.
Remove the pork from the Treager pellet grill and let it rest, covered in foil, for about an hour.
Remove the top bark layer and chop it up to add it to your pulled pork. Pull the pork, removing large chunks of fat as you go.
Serve it as is or with your favorite sauce!