Add the pork shoulder chunks, sliced onion, minced garlic, apple cider, smoked paprika, cumin, salt, and black pepper to the slow cooker. Stir to coat the meat evenly.
Cover and cook on low for 8 hours until the pork is very tender and pulls apart easily.
Remove the pork from the slow cooker and shred it with two forks. Return the shredded pork to the cooker and stir it into the juices.
In a mixing bowl, combine the shredded cabbage, sliced apple, apple cider vinegar, honey, and a pinch of salt. Toss until the slaw is evenly coated.
Warm the corn tortillas in a dry skillet or microwave. Fill each tortilla with pulled pork and top with a generous scoop of cabbage slaw.
Garnish with fresh cilantro and serve with lime wedges on the side.