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 and let cool. Strain out ginger slices.
02 - Blend peaches with lemon juice in a blender until completely smooth.
03 - Combine peach puree and 1/4 cup ginger syrup in a pitcher. Stir thoroughly to incorporate.
04 - Fill four glasses with ice. Pour equal portions of peach-ginger mixture into each glass.
05 - Top each glass with 1/2 cup sparkling water, stirring gently to combine.
06 - Decorate with fresh peach slices and mint sprigs if desired. Serve immediately.