In a medium saucepan, combine sliced ripe peaches, freshly sliced ginger, cane sugar, and 1 cup of water. Place over medium heat and bring to a gentle simmer. Cook for about 5 minutes until peaches are tender and fragrant.

Once the mixture has cooled slightly, transfer it to a blender and blend on high until smooth. Strain the blended mixture through a fine mesh strainer into a large pitcher.

Stir in the freshly squeezed lemon juice to the strained peach liquid. Add the remaining cold water to thin out the concentrate to your desired strength.

Fill tall glasses with ice cubes and pour the Ginger Peach Lemonade over them. Garnish with lemon slices and serve immediately.