01 - Combine ginger, sugar, and water in a small saucepan. Bring to a boil over medium heat, stirring until sugar dissolves. Reduce heat and simmer for 3 minutes. Remove from heat, let cool, then strain out ginger slices.
02 - Blend peaches with lemon juice in a blender until completely smooth.
03 - Pour peach puree into a pitcher. Add 1/4 cup of the prepared ginger syrup and stir thoroughly to incorporate.
04 - Fill four glasses with ice cubes. Distribute the peach-ginger mixture evenly among glasses, about 1/4 per glass.
05 - Top each glass with 1/2 cup chilled sparkling water. Stir gently to combine without losing carbonation.
06 - Decorate each glass with fresh peach slices and mint sprigs if desired. Serve immediately while chilled.