In a medium saucepan, combine chopped peaches, sugar, and 2 cups water. Bring to a simmer over medium heat and cook for about 10 minutes, until the peaches are soft and fragrant.

Remove from heat and let cool slightly. Strain the mixture through a fine-mesh sieve into a large pitcher, pressing down on the solids to extract as much juice as possible.

Add the freshly squeezed lemon juice to the pitcher, followed by 2 to 4 cups of cold water, depending on your desired strength and sweetness. Stir well to combine.

Taste and adjust with more sugar, lemon juice, or water as needed.

Serve over ice, garnished with peach slices and fresh mint for an extra burst of freshness.