Mix the paprika, brown sugar, salt, garlic powder, onion powder, black pepper, mustard and cayenne.
Reserve 1 tablespoon of the rub, then coat the pork thoroughly with the rest.
Spread the onion in a 6-quart slow cooker, add the pork and pour the apple juice and vinegar around the meat.
Cover and cook on low until the shoulder is very tender, about 8 hours.
Transfer the pork to a rimmed pan, discard excess fat and pull the meat into thick shreds.
Toss the pork with the reserved dry rub and 1/2 cup skimmed cooker juices.
Spread half the pork on a foil-lined sheet and broil 3 to 4 minutes until scattered edges brown, then mix it back with the soft pork.