Wash and pit the peaches. Cut into chunks; peeling is optional.

In a medium saucepan, combine peach chunks, sugar, and 1 cup water. Bring to a simmer over medium heat, stirring occasionally. Cook until peaches are very soft and syrupy, about 8-10 minutes.

Carefully transfer the hot peach mixture to a blender or use an immersion blender. Blend until completely smooth. Let cool slightly.

Pour the peach puree through a fine mesh strainer into a large pitcher, pressing to extract all liquid. Discard or save the pulp.

Juice the lemons until you have 1 cup (240ml) fresh lemon juice. Remove any seeds.

Add lemon juice and 3 cups cold water to the pitcher with peach syrup. Stir well. Taste and adjust sweetness or dilution as needed.

Refrigerate until icy cold, at least 1 hour. Alternatively, serve immediately over plenty of ice.

Garnish with lemon slices, peach slices, and mint leaves before serving if desired.