Cut the pork shoulder into large chunks, removing any excess fat. Season the pieces generously with salt, pepper, cumin, and oregano.
In a large pot or Dutch oven, heat the olive oil over medium heat. Sear the pork pieces until browned on all sides, about 3-4 minutes per side.
Add the garlic cloves, orange juice, lime juice, bay leaves, and water to the pot. Stir to combine and bring the mixture to a simmer.
Reduce the heat to low, cover the pot with a lid, and cook for 2-3 hours, stirring occasionally, until the pork is tender and easily shredded.
Once the pork is cooked, remove the lid and increase the heat to medium-high. Let the liquid reduce while stirring the pork to allow it to crisp up in its own fat.
Serve the crispy pork carnitas in warm tortillas with your choice of toppings such as diced onions, chopped cilantro, salsa, and lime wedges.
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