Wash, pit, and dice 6-8 ripe peaches.

In a medium saucepan, combine the diced peaches, 1/2 cup granulated sugar, 1/2 cup water, and 1 tablespoon fresh lemon juice.

Simmer over medium-low heat for 10-15 minutes, stirring occasionally, until the peaches are very soft.

Remove from heat, mash the peaches thoroughly with a fork, then strain the mixture through a fine-mesh sieve into a large bowl to extract a smooth peach puree.

Discard any solids and allow the peach puree to cool completely to room temperature.

In a small saucepan, combine 1 cup granulated sugar and 1 cup water.

Heat over medium heat, stirring constantly until the sugar is completely dissolved. Remove from heat and let cool completely.

Juice 8-10 medium lemons to yield about 1 1/2 cups of fresh lemon juice; strain to remove any seeds or pulp.

In a large pitcher, combine the cooled simple syrup with the strained lemon juice. Stir well to combine.

Add the cooled peach puree to the lemonade base in the pitcher. Stir vigorously to combine.

Begin by adding 4 cups of cold water, taste, and adjust sweetness by gradually adding more cold water (up to a total of 6 cups).

Refrigerate the peach lemonade for at least 30 minutes to thoroughly chill.

Serve over plenty of ice, garnished with fresh peach slices, lemon wheels, and mint sprigs.