Trim and prep the pork: Pat the pork shoulder dry.
Trim thick exterior fat, but leave some for flavor. Cut into 2–3 large chunks if needed to fit your slow cooker.
Mix the rub: In a small bowl, combine brown sugar, salt, black pepper, smoked paprika, garlic powder, onion powder, and cayenne (if using).
Season generously: Rub the spice mixture all over the pork, pressing it in so it sticks.
Make the braising liquid: Stir together apple cider vinegar, broth (or water), Worcestershire, and 1/2 cup BBQ sauce.
Load the slow cooker: Place the seasoned pork in the slow cooker. Pour the braising liquid around the meat, not directly on top, to keep the rub intact.
Cook low and slow: Cover and cook on LOW for 8–10 hours or HIGH for 4–6 hours, until the pork shreds easily with two forks.
Make the slaw: In a bowl, whisk mayo, 1 tablespoon vinegar, Dijon, sugar or honey, salt, and pepper.
Toss with coleslaw mix. Chill until serving.
Shred the pork: Transfer the cooked pork to a large bowl and shred with two forks, removing any large fat pieces.
Reduce and sauce: Skim excess fat from the cooking liquid. Stir in remaining BBQ sauce to taste (start with 1/2 to 1 cup).
Add enough of this saucy liquid to the shredded pork to make it moist and glossy.
Toast the buns: Warm a skillet over medium heat. Spread a little butter on the cut sides of the buns and toast until golden.
Assemble: Pile pork onto buns, top with slaw, and add pickles if you like. Serve extra sauce on the side.