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If you have a food processor: Add the orange juice, cilantro leaves, mint leaves, and smashed (not minced) garlic cloves, and pulse until everything is finely chopped. Add this mixture to a ziplock bag, along with the rest of the oil, zest, lime juice, oregano, and cumin.
If you don't have a food processor: In a large ziplock bag, combine olive oil, orange zest, orange juice, lime juice, chopped cilantro, chopped mint, minced garlic, oregano, and cumin. Shake it around a bit to mix it up, then add the pork shoulder.
Place the zipped up bag in a baking dish, and put it in the fridge overnight, or several hours at least.
Preheat oven to 425 degrees F. Place a wire rack (I used a cooling rack) over a rimmed baking sheet.
Place the pork on the rack and discard the marinade. Salt and pepper the pork well.
Roast the pork for 30 minutes. It should be lightly browned.
Turn the oven down to 375 degrees F. Roast for another 1 hour and 20-30 minutes, or until a meat thermometer reads 160.
Transfer to a cutting board, cover with aluminum foil and let rest at least 20 minutes.
Carve against the grain and serve.