Step 1

Heat the water, sugar, and mint leaves in a saucepan over medium heat, and stir until the sugar is dissolved. Bring the mixture to a boil, reduce heat, and simmer for 3 to 5 minutes to extract the mint flavor. Set the mixture aside to cool, and strain out the mint leaves.

Step 2

Pour the cooled mint mixture, lime zest, lime juice, sparkling water, and rum into a bowl and mix well. Pour into the container of an ice cream maker, and freeze according to the manufacturer's instructions. Serve immediately for a softer texture, or freeze in a sealed container for a harder sorbet. Let hard-frozen sorbet thaw a few minutes before serving.