Place the sliced onion and minced garlic in the bottom of the slow cooker.
Set the pork shoulder on top of the onions and garlic.
Sprinkle the smoked paprika, salt, and black pepper over the pork.
Pour the barbecue sauce and ½ cup apple cider vinegar over the meat.
Cover and cook on low for 8 hours until the pork shreds easily with two forks.
While the pork cooks, combine the shredded cabbage and carrot in a large bowl.
In a small bowl, whisk together the mayonnaise, 2 tablespoons apple cider vinegar, honey, celery seed, salt, and black pepper.
Pour the dressing over the cabbage mixture and toss until evenly coated.
Shred the cooked pork directly in the slow cooker and stir it into the juices.
Spoon the pulled pork onto the buns and top each sandwich with a generous scoop of coleslaw.