Line a shallow dish or pie plate with plastic wrap. Strain the juice off the pears and to the juice add sugar, ginger, lime zest and lime juice. Stir until sugar is dissolved. Spread pear pieces in a single layer in pie plate. Pour juice over pears and freeze for at least 6 hours.
Flip over pie plate onto a cutting board to remove pears and remove plastic wrap. Cut into large chunks and place in a food processor. Puree until smooth. Add chopped mint and pulse until combined. Spread pureed pears into a clean container and freeze for at least an hour. Scoop into dishes and garnish with additional mint leaves if desired. Serve immediately.
Puree can be made and frozen covered for up to two days in advance.