Place one mango on a cutting board with the narrow side facing you. With a sharp knife, slice off one side, sliding the knife along the flat seed. Repeat on the other side of the mango. With a paring knife, make crisscross cuts through the flesh, cutting up to but not through the skin. Repeat with the second mango. Sprinkle 1 teaspoon brown sugar over each mango half, then drizzle each one with 1 teaspoon rum (or orange juice). Set mango halves on a broiler pan or baking sheet. Broil until tops are light golden, 5 to 7 minutes. Serve with lime wedges.