In a small saucepan, combine the water, sugar, and 1 cup mint leaves over medium heat. Bring to a boil, reduce heat, and simmer, stirring occasionally, until the sugar has dissolved, about 5 minutes. Remove the pan from the heat and allow the syrup to cool, about 20 minutes. Strain before using.
In a blender, puree the cooled syrup, cantaloupe, and lime juice until smooth. Taste, and adjust the sweetness by blending in 1 extra tablespoon of sugar at a time. Add the remaining mint leaves and blend until finely chopped. Pour the mixture into a 9-by-13-by-2-inch glass baking dish and freeze until firm, at least 8 hours or overnight.
Use the tines of a fork to scrape the granita into chilled bowls and serve.
Recipe courtesy of Giada De Laurentiis