Cut pork butt into 4 equal cubes. 30 minutes before cooking, season all sides with BBQ rub, reserving 1 Tbsp for later.
Set up the BBQ for indirect cooking (leaving one side of the BBQ off and the other side on full blast).
Fold 1 square foot of tinfoil into a make-shift bowl with holes in the bottom and place it on the hot side of the grill. Place a handful of wood chips in the bowl and wait until they start to smoke. The cold side of the grill should be 250⁰F.
Once the wood chips are smoking, place the mini pork butts on the cold side of the grill. Check the wood chips every 10 minutes to make sure they are still smoking; add more word as needed.
After one hour of smoking, stop feeding with wood. Continue to cook at 250⁰F for another 2 hours.
After 2 hours wrap the pork chunks individually TIGHYLY with tinfoil with 1 Tbsp of the butter. continue to cook for approximately 1-2 hours. Pork is finished once it reaches the internal temperature of 195⁰F (or fork shreddable tender).
Remove from the BBQ and let it sit in the foil for minimum 20 minutes.
Break/Shred into bit size chunks and top with remaining seasoning.
Toast buns. Place desired amount of pork then BBQ Sauce, Pickles, and Slaw and assemble.