Toss the peppers, onion, green onions, ginger, garlic, sugar and spices into a food processor. Blend until everything roughly combines. As the machine runs, add soy sauce, rum, lime juice and olive oil. When you remove the lid from the food processor, it will smell intensely peppery. Don’t worry. This is normal. Reserve ½-1 cup of marinade, depending on the size of your pork.
Pierce 1-inch slits throughout the top of the pork butt. Turn over and repeat on the bottom. Pour the marinade over the pork and turn a few times to ensure it’s well-coated. Gently use your fingers to get some marinade into the slits. Refrigerate covered at least overnight or up to 24 hours.
If you have time, take the pork butt out of the refrigerator for an hour before cooking to help it come down in temperature.
Heat oven to 250 degrees. Remove excess marinade from the pork. Cover a roasting pan with foil. Place on a roasting rack that's been well-coated with cooking spray. Using a wide-mouth meat injector, inject the reserved marinade throughout the pork.
Roast uncovered in the oven until a knife or fork can easily pierce and twist into the meat with little resistance. For a 4-pound roast, this should take about eight hours. For a 7- to 8-pound roast, allow for at least 10 hours of cooking time, though it could take up to 12, depending on the cut. If you prefer to cook to an internal temperature, cook to a minimum of 180 degrees or up to 205 degrees for an even more shreddable texture.
Cover with foil and let the meat rest for 15 minutes. Shred with two forks and serve. Enjoy!