Combine sugar and water in a small saucepan over medium-low heat; cook until sugar is dissolved. Cool to room temperature.
Purée melon chunks until smooth in a food processor or blender. Stir in TABASCO® Green Sauce, lime juice, lime peel, and sugar mixture. Pour mixture into a shallow pan. Freeze 4 to 5 hours, stirring occasionally, until mixture is frozen, granular, and slightly slushy.
Makes 5 cups.