Begin by preparing the sugar syrup. Combine the water and sugar in a saucepan over low heat. Stir with a spoon until the sugar has completely dissolved. Continue cooking over very low heat to prevent it from coming to a boil. After a few minutes, remove from the heat and allow the syrup to cool completely.
Cut the melon in half, scoop out all the seeds and fibers, then slice it into quarters. Remove the rind and dice the melon. Transfer the melon pieces into a blender or food processor and blend until you achieve a smooth, semi-liquid purée.
Pour the purée into the container with the cooled syrup. Blend thoroughly using an electric whisk (or vigorously with a spoon) until the mixture is completely uniform and combined.
Place the mixture into the freezer to chill for 30 minutes. Once chilled, pour the base into an ice cream maker and churn for about 20 minutes. Serve garnished with fresh mint leaves.
