Cut a few slashes in a crosshatch pattern across the fat cap of the pork butt. Rub mustard on top. Massage BBQ rub into the meat, getting it into the cuts. Wrap with plastic wrap and refrigerate, 8 hours to overnight.
Preheat a smoker to 250 degrees F (120 degrees C). Add wood chips according to manufacturer’s instructions.
Place pork butt on rack, with a drip pan underneath to minimize the mess. Smoke until internal temperature of meat reaches 200 to 203 degrees F (93 to 95 degrees C), 10 to 16 hours, depending on size of pork butt and outside temperature.
Remove pork butt from smoker, wrap in foil, and let rest for 1 hour. Remove bone and shred pork.