Apple Pie Granita

Low Cal and healthy!!

3 cups natural-style apple juice
1/2 cup sugar
1 1/2 tablespoons fresh lemon juice
1/2 teaspoon ground cinnamon
Pinch of freshly grated nutmeg
Pinch of ground allspice

In a saucepan, combine all of the ingredients and cook over moderate heat, stirring, until the sugar has dissolved, 3 minutes. Pour into an 8-inch square glass baking dish. Freeze until icy around the edges, about 1 hour. Using a fork, scrape the icy shards into the center. Continue to freeze, stirring occasionally, until slushy throughout, about 3 hours longer. Scoop into bowls and serve.