1Preheat the oven to 350°F. Place a 2 1/4- to 2 1/2-quart soufflé dish in the oven to heat. Combine the sugar and water in a small, heavy saucepan. Cook over medium-high heat until the sugar dissolves, stirring frequently. Continue cooking 3 minutes or until a golden caramel forms, stirring constantly. Protecting your hands, remove the soufflé dish from the oven and pour the caramel inside. Tilt the dish until the caramel thickens and evenly coats the bottom and 1 to 2 inches of the sides. Cool completely. Bring a kettle of water to boil.
2Combine the rum and remaining ingredients in a large bowl, stirring with a whisk until well blended. Pour into the prepared soufflé dish.
3Set the dish into a 9-inch square baking pan; add hot water to the baking pan to come 1 inch up the sides of the soufflé dish.
4Bake until the custard barely jiggles when shaken and a knife inserted halfway between the center and the edge comes out clean, 1 to 1 1/4 hours. Remove the dish from water and let cool on a rack, then chill, covered, at least 4 hours.
5Run a thin metal spatula around inside of the dish, then invert onto a deep plate. Set the soufflé dish in hot water for 10 minutes to loosen the caramel (not all will come off); scrape the caramel over the flan. To serve, cut the flan into wedges.