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 remaining solids.
03 - Add the cold water to the strained peach-lemon concentrate in the pitcher. Stir thoroughly until fully combined.
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.
05 - Fill serving glasses with ice cubes and pour the chilled peach lemonade over the top. Garnish each glass with peach slices, lemon slices, and fresh mint leaves as desired.