Begin by preparing the syrup. Combine the sugar and water in a pot over medium heat. Stir occasionally as the sugar dissolves, then allow the mixture to come to a boil. Let it simmer for about a minute, or until it reaches a temperature of 220°F. If you don’t have a thermometer, ensure the sugar is completely dissolved before boiling briefly. Remove the syrup from the heat and allow it to cool completely. For faster cooling, you can place the pot in the refrigerator.
To make fresh pomegranate juice, slice open 3 pomegranates and carefully remove the seeds. Transfer the seeds to a food processor and pulse on high for several minutes until thoroughly crushed. Strain the mixture through a fine-mesh sieve, pressing firmly to extract as much juice as possible. Measure out 500g of juice for the sorbet and set aside. Any excess juice can be enjoyed as a refreshing drink.
In a large mixing bowl, combine the pomegranate juice, the cooled syrup, and the lime or lemon juice. Stir until well blended. Chill the mixture in the refrigerator for several hours until it is fully cooled.
Once the mixture has chilled, pour it into your ice cream maker and churn according to the manufacturer’s instructions. The result is a smooth, vibrant sorbet bursting with the natural flavor of fresh pomegranates. Serve immediately or transfer to a freezer-safe container for later enjoyment.