To make the Mint Simple Syrup: Combine water and sugar in a small sauce pan. Bring to a boil, stirring the sugar to dissolve. Lower heat, cover and simmer for about 5 minutes. Turn off heat, drop in the mint leaves. Let it cool in the refrigerator for at least 1-2 hours. Strain.
In a tall glass glass, muddle the mint, lime and simple syrup. Stir in the pureed kiwi and rum. Add the ice and top with club soda. Stir again, and garnish with mint and kiwi. Cheers!