Soak raw rice in plenty of water for 30 minutes. Rinse the rice by stirring it with your fingers, draining, and refilling with water. Stir-drain-refill a couple or three times, finally draining most of the water away until the rice is covered by just about a quarter inch of water, then microwave on high, covered, for ten minutes.
Divide the coconut milk; half of a 13.5 oz. can to make the rice sauce and the other half to make the cream sauce.
To make the rice sauce, stir 1/2 can of coconut milk into the cup of sugar and pinch of salt until salt and sugar are dissolved. Pour over rice after it has finished cooking and stir gently but thoroughly to blend. (I feel that this makes a little too much sauce; I pour about 3/4 of it in and discard the remainder.) If you want to form the rice into individual servings, do it now so they have time to firm up (at least half an hour).
To make the cream sauce, dissolve the corn starch, salt and sugar in the other half of the can of coconut milk. Heat in a sauce pan, uncovered, on the stove top until bubbling, stirring frequently to avoid scorching.
Peel and slice the mangoes, arranging around the servings of rice. (It's important to choose well-ripened fruit, so it's nice and soft and sweet.) Drizzle cream sauce over rice and mango slices and serve warm or cold.