In a tall glass or cocktail shaker, place the kiwi slices, reserving a few for garnishing, and muddle or smash with a spoon until only a few pieces remain. Divide the muddled kiwi between two cocktail glasses. Add ice to the glasses. In the shaker, add the lime juice, mint leaves, and simple syrup. Muddle the mint leaves in the juices. Stir or shake to combine. Add the rum and mix one more time.
Divide this mixture into the two glasses with kiwi and ice. Pour 4 ounces sparkling water into each glass, then garnish with kiwi slices and a few mint sprigs. ~Enjoy!