01 - Combine the peeled peach slices and freshly squeezed lemon juice in a blender. Blend on high until completely smooth and no chunks remain.
02 - Pour the blended mixture through a fine mesh sieve into a large pitcher. Use the back of a spoon or spatula to press firmly and extract as much liquid as possible. Discard the remaining 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 incorporate all the liquids.
05 - Taste the lemonade and adjust the balance by adding more sugar for sweetness or additional lemon juice for acidity as desired.
06 - Fill serving glasses with ice cubes. Pour the peach lemonade over the ice and garnish each glass with fresh peach slices, lemon wheels, and mint leaves. Serve immediately.