Mix sugar and water in a small pot and boil for 3 minutes. Let cool.
MAKE THE ICE CUBES:
In a medium bowl, stir together the cooled simple syrup, lemon juice and chopped mint. Pour the mixture into an ice cube tray and freeze.
ASSEMBLE THE COCKTAILS:
In a blender, blend together the frozen cubes, vodka and sparkling water- add a little bit of water at a time until you reach your desired thickness of the drink. Pour into chilled glasses, and garnish with mint sprigs and lemon zest.
Notes
It's also an option to serve this cocktail over ice in a glass (skip making the ice cubes and blending).