In a blender, combine the chopped peaches, sugar, and ground cardamom. Blend until smooth.

Strain the peach mixture through a fine mesh sieve into a large pitcher to remove the pulp, pressing down with a spatula to extract as much juice as possible.

Add the fresh lemon juice and cold water to the pitcher. Stir well to combine.

Taste the lemonade and adjust sweetness if necessary by adding more sugar or water.

Chill the lemonade in the refrigerator for at least 30 minutes before serving.

Serve over ice and garnish with fresh mint leaves if desired.