Preheat the Oven: Preheat your oven to 150°C (300°F).
Prepare the Pork Rub: In a small bowl, combine the salt, black pepper, paprika, garlic powder, onion powder, dried thyme, dried oregano, and brown sugar. This mixture will be used to season the pork.
Season the Pork: Rub the pork shoulder all over with the vegetable oil. Then, generously rub the spice mixture over the entire surface of the pork.
Cook the Pork: Place the seasoned pork shoulder in a roasting pan or Dutch oven. Pour the chicken or beef broth into the pan. Cover the pan with a lid or aluminum foil.
Slow Roast: Roast the pork in the preheated oven for 5 hours, or until the meat is tender and easily pulls apart with a fork. You can baste the pork with the pan juices every hour or so.
Shred the Pork: Once the pork is done, remove it from the oven and let it cool slightly. Then, use two forks to shred the meat into small pieces.
Make the Coleslaw: In a large bowl, combine the shredded cabbage, grated carrots, mayonnaise, apple cider vinegar, sugar, salt, and pepper. Mix well until all the ingredients are evenly coated. Chill the coleslaw in the refrigerator.
Assemble the Sandwiches: Split the burger buns or sandwich rolls in half. Toast them in the oven for a few minutes until they are lightly browned. Then, spoon a generous portion of the pulled pork onto the bottom half of each bun. Top with coleslaw and drizzle with barbecue sauce.
Serve: Place the top half of the bun on each sandwich to complete it. Serve your pulled pork sandwiches hot with extra barbecue sauce and your favorite side dishes.Enjoy your homemade pulled pork sandwiches!