With a sharp knife, lightly score the pork loin by making diagonal cuts 1/4 inch deep at 1-inch intervals on the fat side. Place the pork scored side up in a shallow roasting pan just large enough to hold it comfortably.
If you prefer to use a meat thermometer, insert it into the loin after you have scored the fat side. Be sure the tip of the thermometer does not touch any fat or bone.
Roast the loin in the middle of the oven for 1 hour, or until the pork is golden brown. Remove the pan from the heat and transfer the loin to a cutting board or platter. Skim the fat from the juices in the pan, pour in the stock, and set the pan and its liquid aside.
With a large mortar and pestle or in a small bowl with the back of a spoon, mash the brown sugar, 2 tablespoons of dark rum, garlic, ginger, cloves, bay leaf, salt and pepper to a smooth paste. With a metal spatula or your fingertips, spread the paste evenly over the scored side of the pork.
Return the loin to the pan scored side up and roast in the middle of the oven for another 30 minutes, or until the surface is crusty and brown. (The thermometer should reach a temperature of 160°F to 165°F.).
Transfer the loin to a heated platter and let it rest for 10 minutes for easier carving.
Meanwhile, slowly warm the light rum in a small skillet over low heat. Off the heat, ignite the rum with a match, then slide the skillet gently back and forth until the flames completely die out.
Bring the liquid remaining in the baking pan to a boil over high heat.
Mix together arrowroot and water, and add it to the pan. Stirring constantly, cook briskly until the sauce thickens enough to coat the spoon heavily.
Remove the pan from the heat and stir in the flamed rum and the lime juice. Taste for seasoning and pour the sauce into a heated bowl or sauceboat.