Combine rub ingredients and evenly coat roast. Wrap with plastic wrap and refrigerate for at least 6 hours and up to 48 hours.
Smoke, roast or grill (covered) at 250 degrees for 6 to 8 hours or until the internal temperature away from the bone is 180 degrees. If desired, first brown the roast evenly in a hot oven or on a hot grill. This will give the roast additional flavor and extra crunch on the edges.
Place the roast on top of two or three long sheets of heavy-duty foil. Pour barbecue sauce over roast and wrap snugly with foil so that sauce will not run out. Place back in the 250 degree oven, smoker or grill for another two hours.
Note: Do not try and save money by using standard-grade foil or going short on the foil sheets. Standard grade foil tears easily and the sauce will run out.
Remove roast and allow to cool enough to handle. Shred meat with fingers, tongs, or forks.