Crush the garlic in a mortar with a pestle until it’s creamy. Or use a food processor. Add salt, oregano, cumin, and ground pepper, and then slowly add the citrus juice, while mixing with a spoon. Set your mojo aside.
Put the pork shoulder on a baking tray with the skin side up. Pat it dry with paper towels. Sprinkle some salt on top and rub it in, then turn it upside down so that the meaty side is on top. Cut off pieces of excess skin and fat.
Pierce the meat with a knife in the muscular parts, until it reaches the bone. Now, place a spoonful of marinade into each hole you made and poke it in with your fingers. Then coat the whole pork with marinade and rub it in. Pour the rest of the marinade on top, cover it with plastic wrap and let it marinate in the fridge for at least 12 hours.
Remove it from the fridge 1 hour before cooking.
Place the pork shoulder on a separate tray and pour 2/3 of the mojo juice on it. Then place a wire rack on the initial baking tray and lay the pork shoulder meaty side down on the rack. Dry the skin of the shoulder with paper towels.
Sprinkle a tablespoon of salt on the skin, rub it well, and then pour water slowly and rub it clean.
Dry it again and cover it with aluminum foil with the shiny side down. Preheat the oven to 325F and bake for 1 hour, then turn the heat up to 350F and bake for 2 more hours.
Take it out of the oven and remove the aluminum foil. Turn the oven up to 375F and bake for 1 hour uncovered. Once cooked, measure the internal temperature. When it’s done, it should be around 175F.
Remove from the oven and let rest for 15 minutes. Now, remove the top crunchy skin and place the shoulder on a cutting board. Cut it with a fork and knife into thin slivers. It’ll be so soft and juicy that it falls off your fork.
Place cut/shredded pork in a large bowl and drizzle some of the mojo from the baking tray on top. Just enough to make it juicy, but not wet. Your tender pulled Cuban pork is now ready to be turned into the best Cuban BBQ pork sliders!