How to Make It
Place garlic, cilantro, oregano, salt, pepper, cumin, and 1/2 cup of the oil in a blender. Slowly add orange and lime juice, and pulse until smooth, 10 to 12 times. Remove 1 cup marinade mixture, and reserve for later use.
Place pig in a container that is large enough to accommodate its size. Thoroughly coat with remaining marinade mixture, rubbing all over pig. Cover container, and chill 8 to 24 hours, basting occasionally.
Preheat oven to 275°F. Place a wire rack in a large, aluminum foil-lined rimmed baking sheet or roasting pan. Remove pig from marinade, and place on rack, discarding marinade.
Inject pig all over with reserved 1 cup marinade mixture, and rub with remaining 1 cup oil. Roast pig in preheated oven until a meat thermometer inserted into the shoulder joint close to the head registers 160°F, about 4 hours, rotating pan, if necessary. Increase oven temperature to 425°F, and roast until skin is golden brown and crispy, about 1 hour. Let rest 20 minutes. Serve immediately.