In the container of a blender, process rum, pineapple chunks, cream of coconut, pineapple juice, Bénédictine, lime juice, and mint leaves until smooth.
Transfer to an airtight container, and freeze until ready to serve, at least 6 hours.
Let stand at room temperature for 15 minutes before serving.
Garnish with lime slices and mint sprigs, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/frozen-louisiana-limeade/