Prepare your dry rub and generously coat the pork shoulder on all sides. If desired, apply the rub the day before, cover, and refrigerate overnight to allow the flavors to penetrate.
Soak the wooden chips in water for 30 minutes, drain them, divide into three equal portions and wrap each in aluminum foil, poking several holes in the top of each packet to allow smoke to escape.
Set up your grill for indirect grilling at 110-120°C (230-248°F).
Place the pork shoulder on the grill away from direct heat with the lid closed. Maintain the grill temperature between 110-120°C (230-248°F). For the first 3 hours, add one packet of soaked wood chips to the direct heat every hour. Continue cooking for a total of 8-10 hours until the thickest part of the meat reaches 74°C (165°F) and the bone pulls out easily.
While the pork cooks, prepare your sauce. Put the sauce ingredients in a saucepan and heat over medium heat, stirring occasionally, then simmer for 5 minutes until hot and spicy. Adjust seasoning to taste if needed.
Remove the pork from the grill, wrap it tightly with aluminum foil, and let it rest for 30 minutes so the juices redistribute throughout the meat.
Using two forks, shred the pork meat and remove any large pieces of fat or tendons. Mix the shredded meat with the sauce.