Peel and slice the peaches and mash them by hand or puree ina blender or food processor.
Add water; mix well. Sweeten to taste with sugar ( Note: you may not need any sugar at all!)
Pour the puree into a 8x8 inch baking pan; cover withplastic wrap and freeze.
When the mix is frozen solid, use the tines of a fork toscrap up the frozen mix. Spoon the frozen “shavings” into another container;cover tightly and store in the freezer.
When you are ready to serve, spoon the granita into serving cups. If you'd like to create a parfait, use stemmed cups and layer with fresh blueberries or blackberries; serve topped with sprigs of mint or basil and enjoy this refreshing treat!