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Place pork shoulder, pork belly, stock, salt, and pepper in a large heavy pot; cover and bring to a boil over medium-low. Reduce heat and simmer until pork is tender and shreds easily, about 2 hours. Uncover; cook 10 minutes to reduce liquid (but not completely). Remove from heat.
Transfer half of pork and pan juices to a large skillet, preferably nonstick, and cook over high until liquid evaporates and pork begins to fry in its rendered fat. Fry, stirring occasionally and pressing on pork with spoon to break up, until browned and just beginning to crisp, 10–15 minutes. Most of the pieces should be bite-size with some smaller shredded and super-crisp bits in the mix. Using a slotted spoon, transfer to a paper towel–lined baking sheet. Cover with foil to keep warm and moist. Repeat with remaining pork.
Serve carnitas with tortillas, onion, limes, avocado, herbs, and cabbage.
Do Ahead: Pork can be braised (do not fry) 3 days ahead. Cover and chill.