Grapefruit Granité with Mangoes and White Rum Mojito

In an 8-inch square glass dish, stir together the grapefruit juice, honey and grenadine. Freeze the mixture until solid, at least 3 hours. Meanwhile, in a food processor, combine the mint leaves, sugar, rum and lime juice and puree. Refrigerate the mojito. About 30 minutes before serving, transfer the granité to the refrigerator to soften. Cut each mango half lengthwise into thin slices. Pour the mojito into shallow bowls. Fan out the mango slices in the bowls and top with large scoops of the granité. Garnish with the mint sprigs and serve.