Preheat smoker or barbecue grill to 250 degrees.
Generously rub 1/2 cup of the beef rub and 1/2 cup of barbecue rub on all sides of pork shoulder.
Insert instant-read meat thermometer in thickest part of pork shoulder.
Place pork shoulder on the smoker with the fat side up. Smoke for 2.5-3 hours.
Spray pork shoulder with organic apple juice every 45 minutes. (Use BPA free spray bottle.)
Place pork shoulder on baking sheet, then place back on smoker for additional 5-6 hours, or until instant-read meat thermometer reads 200 degrees.
Pull pork off smoker and place in cooler. Let sit for 30 minutes.
While pork is still hot, carve pork shoulder into 3×3 inch pieces and place into food processor. Pulse food processor 3-4 times until pork is shredded.
Place pork on plate or gluten free buns. Add barbecue sauce, and enjoy!