Pat the pork shoulder completely dry with paper towels. Place it skin-side down on a clean cutting board.
Carefully loosen the skin from the meat with a sharp knife, leaving one edge attached. Do not remove the skin completely.
Cut several deep, 1-inch slits throughout the meaty side of the pork.
Mash the garlic, salt, oregano, and black pepper into a paste using a mortar and pestle. A small food processor can also be used.
Mix in the olive oil, white vinegar, and lime juice.
Push the garlic marinade inside every slit. Rub the remaining marinade over the meat and underneath the loosened skin.
Return the skin to its original position. Keep the outside of the skin clean and dry so it becomes crispy.
Place the pork skin-side up in a roasting pan. Refrigerate uncovered for at least 12 hours, preferably overnight.
Remove the pork from the refrigerator approximately 45 minutes before cooking.
Preheat the oven to 325°F or 165°C.
Add 1 cup of water to the bottom of the roasting pan. Do not pour water over the skin.
Roast uncovered, skin-side up, for approximately 5 to 5½ hours. Add more water to the pan if the drippings begin to burn.
Cook until the thickest part reaches approximately 190–195°F or 88–91°C for a tender, pull-apart texture. Avoid touching the bone with the thermometer.
Increase the oven temperature to 450°F or 230°C.
Roast for another 10–20 minutes until the skin becomes golden, bubbly, and crispy. Watch carefully to prevent burning.
Remove the pernil from the oven. Loosely cover the meat with aluminum foil without tightly covering the crispy skin.
Let the pernil rest for 30 minutes.
Remove and cut the crispy cuerito into serving pieces. Slice or pull apart the pork and spoon some of the pan juices over the meat.