Combine in a food processor:

Pulse about 10 times, just until the fruit is crushed. Transfer to a bowl and refrigerate for 1 hour.

Stir in:

Stir until the sugar is dissolved, 2 to 3 minutes. Refrigerate the ice cream base until cold, overnight if possible, or quick-chill in an ice water bath.

Pour the base into an ice cream maker and freeze as directed. Transfer to a container with a tight-fitting lid and freeze for at least 4 hours to harden.