Put the sugar and water into a saucepan over medium-high heat and bring to a boil. When the sugar has dissolved, remove from the heat and let cool.
Put the mint leaves into a blender along with the lime juice, rum, and cooled sugar syrup. Blend for about 30 to 45 seconds or until the mint is finely chopped. Pour this liquid into a 9 by 13-inch metal cake pan and put it into the freezer. Scrape the mixture every hour with a fork to break up the ice crystals. After about 4 to 6 hours, depending on your freezer, the pan will be full of mojito ice flakes and will be done. Serve in small, cold bowls or glasses, garnished with reserved mint leaves.
Recipe courtesy George Duran