Place sugar and mint leaves in a food processor; process until blended.
In a large heavy saucepan, whisk eggs, sugar mixture, lemon juice and lemon zest until blended. Add butter; cook over medium heat, whisking constantly, until mixture is just thick enough to coat a metal spoon and a thermometer reads at least 170°. Do not allow to boil. Immediately stir in minced mint.
Transfer to a bowl; cool. Press plastic wrap onto surface of lemon curd; refrigerate until cold. Serve or transfer to covered jars and refrigerate up to 2 weeks.