01 - Combine the sliced peaches, freshly squeezed lemon juice, and granulated sugar in a blender. Blend on high until completely smooth and no chunks remain.
02 - Pour the peach-lemon puree through a fine mesh strainer into a large pitcher, pressing firmly with a spoon to extract as much liquid as possible. Discard the retained solids.
03 - Add the cold water to the pitcher and stir thoroughly until the mixture is well combined and uniform in consistency.
04 - Taste the lemonade and adjust sweetness by adding more sugar if desired. Refrigerate for at least 30 minutes to allow the flavors to meld together.
05 - Fill serving glasses with ice cubes, pour the chilled peach lemonade over the ice, and garnish with fresh peach slices, lemon slices, and mint leaves as desired.