Place the pork shoulder in the slow cooker.
In a mixing bowl, stir together 1 cup apple cider vinegar, ketchup, brown sugar, Worcestershire sauce, smoked paprika, garlic powder, 1 teaspoon salt, and black pepper.
Pour the sauce mixture over the pork.
Cover and cook on low until the pork is very tender and pulls apart with a fork.
Shred the pork directly in the slow cooker and stir it into the sauce.
In a separate bowl, combine the shredded cabbage, shredded carrots, mayonnaise, Dijon mustard, 1 tablespoon apple cider vinegar, honey, and ½ teaspoon salt. Toss until evenly coated.
Spoon the pulled pork onto the sandwich buns and top each with a generous scoop of slaw.