Wash, pit, and chop the peaches. Do not peel them, as the skins provide color and flavor.

In a medium saucepan, combine the chopped peaches, sugar, and 1 cup of water. Bring to a boil over medium-high heat.

Reduce heat to low and simmer for 10-15 minutes, gently mashing the peaches to release their juices.

Remove from heat and strain the mixture through a fine-mesh strainer into a bowl, pressing the fruit to extract all the liquid. Discard the pulp and let the syrup cool.

Juice the lemons to yield 1 cup of fresh lemon juice. Strain out any seeds.

In a large pitcher, combine the cooled peach syrup, fresh lemon juice, and 4 cups of cold water. Stir thoroughly.

Chill in the refrigerator. Serve over ice, garnished with a fresh peach slice, lemon wheel, and mint sprig.