01 - Combine sugar and water in a small saucepan. Heat over medium heat, stirring constantly until sugar completely dissolves. Remove from heat and allow syrup to cool to room temperature.
02 - In a large mixing bowl, whisk together the cooled syrup, lemon juice, pink grapefruit or cranberry juice, lemon zest, chopped mint leaves, and salt until fully incorporated.
03 - Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions until the texture becomes thick and slushy, approximately 20-25 minutes.
04 - Transfer the churned sorbet to a freezer-safe container. Cover tightly and freeze for at least 4 hours or until firm enough to scoop.
05 - Scoop the sorbet into chilled bowls or cones. Garnish with additional fresh mint leaves just before serving.