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In a large, sturdy resealable plastic bag, combine the cilantro, orange and lime juices, garlic, oregano, olive oil, 2 tablespoons of kosher salt and 1/2 teaspoon of pepper. Add the pork shoulder, seal the bag and turn to coat. Transfer the bag to a large baking dish and refrigerate the pork overnight, turning the bag once or twice.
Remove the pork from the marinade and scrape off the garlic and herbs; discard the marinade. Season the pork all over with salt and pepper and transfer to a large enameled cast-iron casserole. Let stand at room temperature for 1 hour.
Preheat the oven to 400°. Roast the pork fat side up for 1 hour, until lightly browned. Reduce the oven temperature to 300° and roast for 4 hours longer, until the pork is very tender and the fat cap is crispy; transfer to a carving board and let rest for 30 minutes. Chop the fat cap into bite-size pieces. Carve, shred or pull apart the pork and garnish with the crispy cap pieces. Serve with lime wedges.