Pat pork dry with paper towels; season liberally with barbecue rub on all sides.

Heat the vegetable oil in a large Dutch oven over medium heat. Brown the pork on all sides, taking care not to get the oil too hot. Remove the meat to a platter. Add onions and garlic to the pot. Cook, stirring occasionally, until the onions are tender (about 10-15 minutes). Stir in 1 ½ teaspoons salt, Dr. Pepper and barbecue sauce. Nestle the pork shoulder in the pot (fat-side up). Cover the pot.

Roast the pork shoulder in a 325°F oven for about 4-5 hours, basting with cooking liquid every hour or so (if possible). The pork is done when the meat is falling off the bone (an internal temperature of about 205°F).

Transfer the pork to a large cutting board or rimmed sheet pan. When it's cool enough to handle, shred the meat with two forks (discarding fatty pieces), and return to the pot with the juices. Serve on rolls with additional barbecue sauce and coleslaw, if desired.

Place the onion and garlic in the bottom of a slow cooker.

Pat pork dry with paper towels; season liberally with barbecue rub on all sides. Nestle the pork shoulder in the slow cooker on top of the onions (fat-side up). Add 1 ½ teaspoons salt, Dr. Pepper and barbecue sauce. Cover and cook on LOW for 10-12 hours, or on HIGH for 5-6 hours, until the pork is fall-apart tender.

Transfer the pork to a large cutting board or rimmed baking sheet. When it's cool enough to handle, shred the meat with two forks (discarding fatty pieces), and return to the pot with the juices. Serve on rolls with additional barbecue sauce and coleslaw, if desired.