Blend the fruit, sugar, honey and lemon juice with 2 cups ice in a food processor or blender until chunky. Add another 1 cup ice and blend until completely smooth.
Pour the mixture into a shallow baking dish and freeze 30 minutes. Scrape the ice with a fork until slushy, then freeze until firm, about 2 more hours. Scoop into paper cups.
Photograph by Levi Brown
Recipe courtesy of Food Network Magazine