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In a small bowl, mix together the salt and paprika. Using a paring knife and a twisting motion, make twelve 1-inch-deep cuts over the pork. Rub the pork all over with the salt mixture, then wrap tightly in plastic wrap and refrigerate 8 to 24 hours.
Heat the oven to 400ºF with a rack in the lower-middle position. In a liquid measuring cup, combine both juices. In a food processor, combine both zests, the oregano, garlic, oil, cumin and pepper.Process until the garlic is finely chopped, about 1 minute. Add ¼ cup of the juice and process until combined, about 10 seconds.
Using 18-inch-wide heavy-duty foil, make a foil sling in a large roasting pan. Leaving a generous amount of overhang on either side, gently press 1 sheet of foil into the pan lengthwise. Press a second sheet over that crosswise, again leaving ample overhang. Using kitchen parchment, repeat this process, setting the sheets over the foil. Set a wire roasting rack over the parchment.
Unwrap the pork and rub all over with the herb-garlic paste. Place fat side up on the rack in the prepared pan. Pour ¼ cup of the juice into the bottom of the pan. Loosely fold the excess parchment around the pork, then fold the excess foil up over the pork. Crimp the foil together to create a loose but sealed packet.Roast until the meat is tender and registers 190ºF, about 3½ hours.
Transfer the pork to a carving board, tent loosely with foil and let rest for 30 minutes. Pour the accumulated juices from the pan into a medium saucepan over medium heat, then add the remaining ½ cup citrus juice.When hot, remove from the heat and stir in the cilantro; cover and keep warm.
Using tongs and a knife or carving fork, cut and shred the meat into chunks, discarding the bone and any fat. Transfer to a bowl and toss with ¼ to ½ cup of the sauce. Serve with the remaining sauce and lime wedges.