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