6 cups water
Pour 6 cups of water into a medium saucepan. Cover and bring to a boil over high heat. Remove from the heat and add 1 cup of mint leaves. Cover and steep for 30 minutes to allow the mint to infuse the water. Strain the mint tea into a pitcher, discarding the leaves, and refrigerate until cold.
Meanwhile, chop 2 peaches coarsely and place them in a blender. Puree until smooth, adding a couple tablespoons of mint tea to help create the puree. Strain the peach puree through a fine-mesh sieve and chill the puree. You should have about 1 cup of puree. It will have a peach color when first blended, and will turn into a brownish tea color once chilled.
Thinly slice the remaining peach. In 4 tall glasses, layer the crushed ice, thin slices of peach, and the remaining 1/4 cup mint leaves, filling glasses about halfway. Divide the chilled mint tea among the glasses, and then stir in the peach puree. Serve immediately.