Prepare the Pork:

• In a small bowl, mix the brown sugar, paprika, black pepper, salt, chili powder, garlic powder, onion powder, cumin, and smoked paprika to create the dry rub.
• Rub this mixture all over the pork shoulder, covering it evenly. Let it sit for at least 30 minutes to allow the flavors to absorb (or refrigerate overnight for deeper flavor).

Cook the Pork:

• Preheat your oven to 300°F (150°C).
• Heat olive oil in a large Dutch oven over medium-high heat. Sear the pork on all sides until browned (about 2-3 minutes per side).
• Once browned, remove the pork from the Dutch oven and set it aside.
• In the same pot, add the apple cider vinegar, chicken broth, and Worcestershire sauce, scraping up any browned bits from the bottom of the pan.
• Return the pork to the pot, cover with a lid, and transfer to the preheated oven. Cook for about 3.5 to 4 hours, or until the pork is tender and easily shreds with a fork.

Shred the Pork:

• Remove the pork from the oven and let it rest for 10 minutes.
• Using two forks, shred the pork into bite-sized pieces. Discard any fat and bone (if using a bone-in shoulder).
• If the pork seems dry, you can mix in some of the cooking liquid from the pot to add moisture.

Assemble the Sandwiches:

• Toast the sandwich buns in a skillet or oven until lightly golden.
• Pile the shredded pork onto the bottom half of each bun.
• Drizzle BBQ sauce over the pork (to taste), then top with a generous amount of coleslaw (if desired).
• Place the top half of the bun on each sandwich and serve immediately.