You may substitute 1 cup (about 9 ounces) thawed frozen berry puree for the homemade puree in this recipe.
Combine in a food processor:
Pulse until the fruit is crushed and very juicy. Transfer to a small bowl and refrigerate for 1 hour. Strain the mixture through a fine-mesh sieve, pressing firmly to extract all the berry juices; discard the seeds. Add:
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.