Add sugar and 1 cup water to a sauce pan, stir and bring to a boil. Boil for 5 minutes, then remove from heat and stir in 2 sprigs of fresh mint. Allow to cool to room temperature.
Chop remaining 2-3 mint sprigs. Add the cooled simple syrup to a pitcher. Add the fresh lime juice, cold water, sparkling water and chopped fresh mint leaves. Stir well. Taste for sweetness and add more cold water to dilute, if necessary.