In a medium saucepan, combine the chopped peaches, sugar, and 1 cup of water. Bring to a boil over medium heat, stirring occasionally until the sugar dissolves and the peaches soften, about 5-7 minutes.

Remove the saucepan from heat and let the mixture cool for about 10 minutes. Then, blend the peach mixture in a blender until smooth.

Strain the peach puree through a fine-mesh sieve into a large pitcher to remove any solids, pressing down with a spatula to extract as much liquid as possible.

Add the freshly squeezed lemon juice and 4 cups of cold water to the pitcher. Stir well to combine. Taste and adjust sweetness by adding more sugar if desired.

Chill the peach lemonade in the refrigerator for at least 1 hour before serving. Serve over ice and garnish with fresh mint leaves if desired.