In a small saucepan, bring the water and the mint leaves to a boil. Turn off the heat, cover, and let the mint leaves steep for 5 minutes. Let the mint water cool to room temperature.
Place the mint water (including leaves) peaches, ice cream and 1 cup of ice cubes in a blender and puree until smooth. Serve immediately in chilled glasses and garnish with a slice of peach and a sprig of mint.