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 - Puree the peaches with lemon juice in a blender until completely smooth.
03 - Combine the peach puree and 1/4 cup ginger syrup in a pitcher. Stir thoroughly to incorporate.
04 - Fill four glasses with ice cubes. Distribute the peach-ginger mixture evenly, pouring 1/4 into each glass.
05 - Top each glass with 1/2 cup sparkling water, stirring gently to combine while maintaining carbonation.
06 - Decorate each glass with fresh peach slices and mint sprigs if desired.