- Place the pork on a board and pat dry with paper towels, if needed. Place the pork on a rack in a heavy roasting pan. Using the tip of a sharp knife, make 1-inch-deep incisions all over the surface of the roast. Insert the garlic slices into the slits.
- In a small bowl, combine the salt, garlic powder, onion powder, coriander, paprika, pepper, and 1 teaspoon each of the allspice and ginger. Use your fingers to press the rub into the roast to completely coat it on all sides. Let rest for 30 minutes or refrigerate, covered, up to 24 hours. (If refrigerated, let stand at room temperature 1 hour before roasting.)
- Preheat the oven to 350°F. Carefully pour about 1 cup water into the bottom of the roasting pan. Set a rack in the roasting pan and the pork on the rack. Cover with foil. Roast for 3 hours, basting every 45 minutes.
- Meanwhile, in a small bowl, combine the brown sugar, rum, lime juice, minced garlic, and remaining ½ teaspoon each of the allspice and ginger. Uncover the roast. Spread the paste over the meat and return it to the oven. Continue to roast until the outside is nicely browned, about 1½ hours, until the internal temperature reaches 185°F and the paste is sealed onto the roast. Let rest 10 minutes before slicing.