Wash and pit 4-5 ripe peaches, then dice into small pieces. In a medium saucepan, combine diced peaches with 0.5 cup granulated sugar, 1 cup water, and 0.25 cup fresh lemon juice. Simmer over medium heat for 10-15 minutes until peaches are soft.

Cool the peach mixture slightly, then mash until smooth. Strain through a fine mesh sieve into a bowl, discarding solids. Let the peach puree cool completely.

In a clean saucepan, combine 1 cup granulated sugar with 1 cup water. Heat while stirring until sugar dissolves and syrup is clear (about 5 minutes). Cool completely.

Juice 6-8 fresh lemons to get about 1.5 cups lemon juice, straining out seeds or pulp. In a large pitcher, mix strained lemon juice with cooled simple syrup.

Gently stir in cooled peach puree to the lemon mixture. Gradually add 4-6 cups cold water until desired sweetness and strength is achieved.

Refrigerate for at least 30 minutes. Serve over ice garnished with fresh peach slices, lemon wheels, and mint sprigs.