Black rice, rich in immune-boosting vitamin E, has more anthocyanin antioxidants than blueberries.
Combine rice, ¼ teaspoon of the salt and water in a medium saucepan; bring to a boil. Reduce heat to low, cover and simmer until rice is almost tender but still chewy, 30 to 45 minutes. Open coconut milk; carefully scoop off solid cream on top, taking care not to get any liquid. Refrigerate cream.
Stir sugar, remaining ¼ teaspoon salt and liquid coconut milk into rice; bring to a boil over high heat. Reduce heat to low; simmer, uncovered, stirring occasionally, until mixture is thick and rice is tender but still slightly chewy, 15 to 30 minutes. Remove from heat and let cool, stirring occasionally, for at least 30 minutes.
Divide pudding among 8 bowls. Arrange persimmons on top. Sprinkle lightly with sugar, if desired. Whisk coconut cream until soft peaks form. Dollop onto puddings and serve immediately.
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