- Bring 1 cup water to boil in small saucepan. Remove from heat; add mung beans; cover and set aside until beans have softened, about 10 minutes.
- Drain beans and transfer to paper towel–lined plate, spreading into even layer. Let stand at least 5 minutes to dry. Add beans to small skillet and place over medium-high heat.
- Cook, stirring frequently, until beans are just starting to turn lightly golden, 5 to 7 minutes. Transfer to bowl and let cool completely before using. (Toasted mung beans can be stored in airtight container at room temperature for 1 week.)
- Place rice in fine-mesh strainer and rinse under cold running water until water runs clear. Place rinsed rice in medium heatproof bowl and cover with several inches cold water. Let rice stand for at least 1 hour or up to 24 hours. Drain rice well in fine-mesh strainer. Rinse bowl in which rice soaked.
- Bring 4 cups water to boil in 14-inch flat-bottomed wok or 12-inch skillet over high heat. Meanwhile, line steamer basket with clean, damp dish towel. Transfer rice to center of towel and pat rice in even layer. Fold overhang over rice to form bundle and cover with steamer lid. Set steamer in wok and reduce heat to maintain simmer (small wisps of steam should escape from beneath lid). Steam rice until translucent, tender but still chewy, 20 to 25 minutes (check rice by carefully unwrapping bundle; taste rice from center of pile).
- While rice steams, combine 1 cup coconut milk, sugar, and ¼ teaspoon salt in small saucepan over medium heat and cook, stirring frequently, until sugar dissolves. Remove from heat and cover to keep warm.
- Transfer rice to cleaned bowl. Working quickly, pour coconut milk mixture over top (it will look like too much liquid). Stir gently to combine; cover; and let stand until liquid is absorbed, about 15 minutes.
- Meanwhile, rinse saucepan and add remaining coconut milk and remaining ⅛ teaspoon salt. Bring to simmer over medium heat. Combine 1 teaspoon water and cornstarch in small bowl, stirring until cornstarch is dissolved. Stir cornstarch mixture into coconut milk and cook, stirring constantly, until sauce is slightly thickened, 1 to 2 minutes. Remove from heat and set aside. (Cooled sauce may be refrigerated overnight. Bring to room temperature before serving.)
- When ready to serve, divide coconut rice among serving plates. Arrange sliced mango alongside (½ mango per person). Spoon sauce over rice. Sprinkle mung beans over sauce and rice and serve.
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