For the sauce: Combine the oil, molasses, soy sauce, allspice, garlic, Scotch bonnet pepper, scallions, thyme and some black pepper in a blender and blend. Transfer to a saucepan and cook until the sauce changes color, 10 to 15 minutes.
For the ribs: Preheat the oven to 400 degrees F. In a bowl, combine the sugar, caraway seeds, garlic, salt and cayenne pepper. Coat the ribs evenly on both sides and reserve any remaining rub. Sprinkle the ribs with paprika. Place the ribs in a hotel pan or deep baking dish. Cover tightly with foil. Bake covered completely, about 2 hours 30 minutes.
Check the ribs for doneness throughout; when the meat separates from the bone, the ribs are done. Coat the ribs evenly with the jerk sauce and cook, covered, for an additional 15 minutes.