Slice peaches reserving 5-10 for the sides of the glasses. Place sliced peaches and 1 cup of water in a blender and blend until smooth. Add sugar to a pot and turn heat to medium and add blended peaches. Boil for 2-3 minutes or until the liquid clears slightly and sugar has dissolved completely. Let liquid cool.
Once cooled add liquid to a pitcher along with peach balsamic vinegar, ice, and sparkling water. Place some additional ice into each glass and then dip a sliced peach partway into granulated sugar and push onto the sides of the glasses. Pour sparkling peach spritzer into glasses and garnish with a sprig of mint