Mix the dry rub. In a small bowl, combine brown sugar, smoked paprika, salt, pepper, garlic powder, onion powder, ground mustard, and cayenne if using.
Season the pork. Pat the pork shoulder dry. Rub the spice mix all over, pressing it in so it sticks.
Set up your cooker. Add the broth, apple cider vinegar, and gluten-free Worcestershire to a slow cooker.
Place the pork on top, fat side up.
Cook low and slow. Cover and cook on Low for 8–10 hours, or on High for 5–6 hours, until the pork is very tender and shreds easily with two forks.
Make the sauce. While the pork cooks, stir together the gluten-free ketchup, vinegar, sweetener, Worcestershire, smoked paprika, garlic powder, onion powder, black pepper, and optional cayenne. Simmer for 5–10 minutes on low to meld flavors, then set aside.
Shred the pork. Transfer the cooked pork to a large bowl. Skim excess fat from the cooking liquid.
Shred the meat with two forks, discarding large fatty bits.
Moisten and sauce. Add 1/4–1/2 cup of the reserved cooking juices to the shredded pork for moisture. Stir in 1/2–3/4 cup of the BBQ sauce, tasting and adding more as you like.
Toast the buns. Lightly toast gluten-free buns to improve structure and flavor. This helps them stand up to saucy fillings.
Assemble. Pile pulled pork onto buns, top with slaw, and add pickles or jalapeños if you like extra bite.
Serve. Offer extra sauce on the side.
Keep napkins nearby—this is wonderfully messy.