Begin by washing, pitting, and dicing 6-8 large, ripe peaches. In a medium saucepan, combine them with 1/2 cup granulated sugar, 1/2 cup water, and 1 tablespoon fresh lemon juice. Heat over medium and let simmer for 10-15 minutes until softened and fragrant.

Remove from heat and allow to cool slightly. Mash cooked peaches and strain through a fine sieve to create smooth peach puree. Let cool completely, about 15-20 minutes.

In a small saucepan, combine 1 cup granulated sugar with 1 cup water over medium heat, stirring until sugar dissolves and mixture simmers. Cool before using.

Juice about 8-10 medium lemons for 1 1/2 cups of juice, straining to remove pulp. In a large pitcher, combine lemon juice with cooled simple syrup.

Fold cooled peach puree into the lemonade base. Gradually mix in 4-6 cups cold water to reach desired taste.

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