Preheat your oven to 150°C (300°F). In a large bowl, combine the pork shoulder chunks, salt, black pepper, cumin, and oregano. Mix well to coat the pork evenly with the seasoning. This helps infuse the meat with deep, robust flavors.
Heat a large Dutch oven or heavy-bottomed pot over medium heat. Add the lard (or oil if preferred), and once hot, sear the pork in batches until browned on all sides, about 3-4 minutes per side. This step locks in moisture and adds a rich crust to the pork.
Once the pork is seared, remove it from the pot and set aside. In the same pot, add the quartered onion, garlic, bay leaves, cinnamon stick, and the reserved orange peel. Cook for about 2-3 minutes until fragrant, which builds the aromatic base of the carnitas.
Return the seared pork to the pot, nestling it among the onion and spices. Pour in the fresh orange juice and water to deglaze the pot, scraping any browned bits from the bottom to enhance the flavour.
Cover the pot with a lid or aluminium foil, ensuring a tight seal, and transfer it to the preheated oven. Let the pork cook slowly for 3 hours, or until the meat is tender and easily shredded. This low, slow cook method allows the pork to develop its signature melt-in-your-mouth texture.
After 3 hours, check the pork for tenderness. Remove the lid and increase the oven temperature to 200°C (400°F). Cook uncovered for an additional 20-30 minutes to allow the pork to crisp on the edges while remaining tender inside.
Remove the carnitas from the oven and carefully shred the pork using two forks. Discard the cinnamon stick, orange peel, and bay leaves. If desired, toss the shredded pork in the remaining juices in the pot to keep it moist and flavourful.
Serve the carnitas hot with fresh tortillas, salsa, chopped cilantro, and lime wedges. You can also accompany them with pickled onions or guacamole for extra flavour. For added crunch, crisp up some of the carnitas under the broiler for a few minutes before serving.