Prep: 1. Peel, if desired, and slice peaches. Make: 1. Combine all the ingredients in a saucepan over medium heat. Start with 1/2 cup water and 1/4 cup sugar and add more if needed to taste. The mixture should be more watery than syrupy so that it freezes well. 2. Cook, stirring occasionally, until all the fruit has broken down into mush (15-20 minutes). You want a consistency somewhere between pulpy orange juice and applesauce at this point. If needed add more water. 3. Let mixture cool to room temperature and then pour into a shallow baking dish. The more thinly spread the base is, the quicker it will freeze. Put the pan into the freezer. 4. After 1/2 hour, take the pan out of the freezer and rake or stir the granita with a fork. Repeat every half hour until the granita reaches a consistency similar to snow (about 2 hours depending on how thin it is spread in the pan).
This works with any kind of summer fruit! Raspberry, strawberry, and plum are our other favorites. With strawberries and raspberries you may want to strain out the seeds after cooking, but we like the additional texture.