Place the pork shoulder on a small baking sheet and pat it dry with a couple of sheets of paper towel. Set aside.
1 bone-in pork shoulder
In a small bowl whisk to combine the salt, brown sugar, oregano, cumin, garlic powder, and onion powder. Cover the shoulder in the dry rub mixture and wrap it with plastic wrap. Transfer to the fridge and let sit in the dry rub for at least 8 hours, preferrably 12.
1½ tbsp kosher salt, 1 tbsp brown sugar, 2 tsp dried oregano, 2 tsp ground cumin, 1½ tsp garlic powder, 1½ tsp onion powder
Take the pork out of the fridge 1 hour prior to cooking. Preheat the oven to 300°F.
Place a large dutch oven over medium heat. Add the oil and heat until shimmering. Add the pork shoulder to the pot and sear on all sides until golden. Pour in the cola, rum, and lime juice. Place the lid on the pot and place it in the oven. Cook the pork for 2 hours with the cover on. Take the cover off and flip the pork and cook for another hour and a half, flipping the pork once again halfway through.
¼ cup neutral oil, 3 cups cola, ½ cup gold rum, 2 limes
Once the pork is done, let it rest for 15 minutes before transferring to a baking sheet and shredding the meat using two forks. Discard the bones and any excess fat. Spoon some of the braising liquid over the shredded meat to moisten it. Tent the meat in foil and keep warm until ready to serve.