Arrange a 9 x 13-inch baking dish or 9 1/2-cup rectangular plastic container in the freezer, making sure it’s level and secure. Put the sugar and 1 cup water into a medium saucepan. Cook, stirring, over medium heat until the sugar is dissolved, about 3 minutes. Set aside to cool completely or refrigerate for up to 1 day. For faster cooling, set the bowl over a bowl filled with ice and stir occasionally until well chilled.
Cut the melon in half, scoop out the seeds, and cut the flesh into 1- to 2-inch chunks. Pile the melon into a food processor and process until smooth, about 1 minute (you’ll have about 2-1/2 cups). Add the fruit puree to the sugar syrup along with the mint, lime juice, and a pinch of salt and stir until blended. Set aside to cool completely, then refrigerate until chilled or for up to 1 day. For faster cooling, set the bowl over a bowl filled with ice and stir occasionally until well chilled.
Pour the chilled mixture into the baking dish and freeze for about 2 hours. After that, every 30 minutes, stir, smash and scrape the mixture with a table fork until the ice crystals are loose and frozen. Serve garnished with mint sprigs.
To make a sorbet: have ready an ice cream maker. Follow the directions for making the mixture. Arrange a 4-1/2 x 8-1/4-inch loaf pan in the freezer, making sure it’s level and secure. Pour the chilled mixture into the ice cream maker and process according to the manufacturer’s instructions. Serve immediately (it will be soft) or scrape into the chilled loaf pan, cover, and freeze until firm or for up to 2 days.
Photo: Kate Sears