Combine Dominican Seasoning, black pepper, oregano, 2 teaspoons of kosher salt and the juice of half a lime and set aside.
Continue by cleaning off the meat – Rinse off the meat under cold water. Sprinkle half of the remaining salt all over the fat side along with the juice of half a lime. Rub the salt-lime mixture all over the meat with your hands. Repeat on the other side. Then rinse off the salt-lime mixture with cold water.
To season the meat - use a sharp knife to poke multiple holes on all sides. Place the shoulder in a large heavy bottom pot. Then rub the marinade all over the meat. Using your fingers make sure some of it seeps into the incisions. Once the marinade has been evenly distributed all over the meat, pour the juice of 1 lime over the top. Cover and let sit in the refrigerator 12-24 hours.
Let the meat sit on the counter for 1 hour before cooking. Then let steam in the covered pot over low heat for 3 hours on top of the stove.
After 2.5 hours, preheat the oven to 350 degrees.
Transfer the meat to a roasting pan and pour half of the liquid in the bottom of the pot over the meat. (Reserve the remaining liquid.) Then transfer to an oven and roast uncovered for 3 hours. To ensure that the skin remains crunchy, every hour pour ½ - ¾ cups of the liquid over just the meat, not the skin, to baste.
Your shoulder is done when the meat pulls away from the interior bone. You can also test for doneness by inserting a table knife or fork into the meat the check for tenderness.
Let sit for 10-15 minutes before shredding and serving.