Trim any excess thick layers of fat from the pork shoulder and pat dry with a paper towel.
In a small bowl, whisk together the smoked paprika, garlic powder, onion powder, sea salt, and black pepper.
Rub the spice mixture evenly over all sides of the pork shoulder.
Place the seasoned pork into the slow cooker and pour the apple cider vinegar and water around the base of the meat.
Cover and cook on low for 8 to 10 hours, or until the pork is tender enough to be easily pulled apart with a fork.
Remove the pork from the slow cooker, discard the cooking liquid, and shred the meat using two forks, removing any remaining gristle.
Toss the shredded pork with the sugar-free BBQ sauce until well coated.
In a separate bowl, toss the shredded cabbage with a splash of apple cider vinegar and the dijon mustard to create a quick vinegar slaw.
Lightly toast the sprouted grain bun in a dry pan or toaster.
Pile the BBQ pulled pork onto the bottom half of the bun, top with the crisp slaw, and close with the top bun.