01 - Combine the peach slices and freshly squeezed lemon juice in a blender. Blend on high until completely smooth and no chunks remain.
02 - Pour the blended puree through a fine mesh sieve into a large pitcher, pressing firmly with a spatula or spoon to extract as much liquid as possible. Discard the retained solids.
03 - Add the granulated sugar to the pitcher and stir thoroughly until fully dissolved into the peach-lemon mixture.
04 - Pour in the cold water along with the sparkling water or club soda, if using. Stir well to fully combine all components.
05 - Taste the lemonade and adjust sweetness or acidity as needed by adding more sugar or lemon juice in small increments.
06 - Fill serving glasses with ice cubes and pour the peach lemonade over the top. Garnish each glass with fresh peach slices, lemon wheels, and mint leaves. Serve immediately.