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. Press firmly with the back of a spoon to extract maximum liquid. Discard the retained solids.
03 - Pour the cold water into the pitcher and stir thoroughly until the mixture is fully 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 and develop.
05 - Fill serving glasses with ice cubes and pour the chilled peach lemonade over the top. Garnish each glass with fresh peach slices, lemon rounds, and mint leaves as desired.