Begin by squeezing fresh lemons to extract about 1 cup of juice, discarding the seeds. In a large pitcher, combine the lemon juice with 8 cups of cold water and 1 cup of sugar; stir until the sugar dissolves completely. Chill the pitcher in the refrigerator for at least 30 minutes.

While the lemonade chills, wash 4 ripe peaches under cold water and slice them in half, removing the pit. Cut into thin wedges and reserve about a quarter of the slices for garnish.

In a blender, combine the remaining peach slices with 1 cup of the chilled lemonade and a handful of fresh mint leaves. Blend on high speed until smooth, about 30 seconds. If a thinner texture is preferred, strain the mixture through a fine mesh sieve.

Take the pitcher of chilled lemonade from the refrigerator and pour in the peach mixture, stirring well to combine both flavors fully. Adjust sweetness if needed.

To serve, fill glasses with ice and pour the lemonade over the ice. Garnish with reserved peach slices and fresh mint sprigs.