Cook peaches and water in a covered saucepan on medium heat for about 10 minutes or until soft. Give it a stir a few times. Remove from heat and stir in sugar. Let mixture cool to room temperature. Purée mixture in blender with remaining ingredients (leave some chunks if desired). Chill the mixture thoroughly in the refrigerator or over an ice bath then freeze in your ice cream maker.
Recipe adapted from The Perfect Scoop