In a medium saucepan, combine the sliced peaches, sugar, and 1 cup of water over medium heat.

Bring to a gentle simmer and cook for 10-15 minutes, stirring occasionally, until the sugar is dissolved and the peaches are soft.

Remove from heat and let cool slightly. Transfer the mixture to a blender and blend until completely smooth.

Pour the puree through a fine-mesh strainer into a bowl, pressing with a spoon to extract all the peach syrup while discarding the solids.

In a large pitcher, combine the strained peach syrup and freshly squeezed lemon juice.

Add 3 to 4 cups of cold water, depending on how strong you want the flavor, and stir well.

Chill in the refrigerator. When ready to serve, pour over ice and garnish with fresh peach slices, lemon wheels, and mint sprigs.