- In a bowl, combine all the ingredients until the sugar and salt have dissolved. Set aside.
- In a bowl, combine all the ingredients of the dry rub. Set aside.
- Place the shoulder in a glass dish, big enough to collect the brine. With a food syringe, inject the brine into the meat, pricking all the surfaces of the meat (see note).
- Rub the entire surface of the shoulder with the dry rub.
- Cover with plastic wrap or place the shoulder in a large sealable plastic bag with the collected brine. Refrigerate for at least 12 hours or overnight.
- Meanwhile, in an airtight container, combine all the ingredients.
- Preheat a section of the grill, setting the burner to medium-low.
- Wrap the shoulder with aluminum foil and place on the off section of the grill. Close the lid. Cook for 4 hours, taking care to keep the temperature of the grill around 110 to 120 ° C (225 to 250 ° F). Unwrap the shoulder and place back on the grill. Place the wood chips in an aluminum plate under the lit section of the grill.
- Brush the roast with the flavoured vinegar and cook, covered, basting regularly, for about 1 hour and 30 minutes or until the meat flakes easily with fork.
- Place the roast on a platter and let rest for 15 minutes. With two forks, shred the meat. In a bowl, combine the meat with barbecue sauce, such as Mr. B's Smokin Bar-B-Q sauce or other, to taste. Serve hot in toasted hamburger buns.
As the pork shoulder is not covered with rind, it is best to wrap it with aluminum foil to prevent it from drying out. Food syringes are found in kitchen stores. If you can’t find them, make deep incisions in the meat with a knife.