Place the pork chunks in the slow cooker. Add the minced chipotle peppers, sliced onion, minced garlic, cumin, oregano, chicken broth, salt, and black pepper. Stir to coat the meat evenly.
Cover and cook on low for 8 hours until the pork pulls apart easily with a fork. Shred the meat directly in the slow cooker using two forks and mix it with the cooking juices.
In a large bowl, combine the shredded cabbage, shredded carrot, lime juice, olive oil, and salt. Toss until the vegetables are evenly coated. Set the slaw aside while the pork finishes cooking.
Warm the corn tortillas in a dry skillet or microwave. Fill each tortilla with a portion of the shredded carnitas and top with a scoop of cabbage slaw. Add a few cilantro leaves before serving.