Place the pork shoulder in the slow cooker and add the sliced onion, minced garlic, 1/2 cup apple cider vinegar, salt, and black pepper.
Pour 1/2 cup of the BBQ sauce over the pork and cover the slow cooker.
Cook on low for 8 hours until the pork shreds easily with a fork.
Remove the pork from the slow cooker and shred it with two forks, then return it to the cooker and stir in the remaining 1/2 cup BBQ sauce.
In a mixing bowl, combine the shredded cabbage, shredded carrot, 2 tbsp apple cider vinegar, honey, and mayonnaise to make the slaw.
Spoon the pulled pork onto the sandwich buns and top each with a generous scoop of tangy slaw.