Prep the pork: Trim excess surface fat from the pork shoulder.
Cut into 3–4 large chunks if needed so it fits your cooker.
Mix the sauce: In a bowl, combine BBQ sauce, brown sugar, apple cider vinegar, Worcestershire, mustard, onion powder, garlic powder, smoked paprika, salt, and pepper. Stir until smooth.
Dump and coat: Place the pork in your slow cooker or Instant Pot. Pour the sauce over the top.
Turn the meat to coat every piece. For Instant Pot, add 1/4 cup apple juice or broth.
Cook (Slow Cooker): Cover and cook on Low for 8–10 hours or on High for 4–6 hours, until the pork shreds easily with two forks.
Cook (Instant Pot): Seal and cook on High Pressure for 60–70 minutes (for a 3–4 lb roast), then natural release for 15 minutes before venting.
Cook (Oven Option): Place in a heavy Dutch oven, cover tightly, and bake at 300°F (150°C) for 3–4 hours until fork-tender.
Shred: Transfer the pork to a large bowl. Shred with two forks, discarding large pieces of fat.
Skim excess fat from the cooking liquid if desired.
Moisten and season: Return the shredded pork to the pot with its juices. Taste and adjust seasoning. Add a splash of BBQ sauce if you want it saucier, or vinegar for extra tang.
Serve: Pile onto buns with coleslaw and pickles, or use in tacos, bowls, or baked potatoes.