Step 1Make a boysenberry puree by tossing the berries and the sugar together and setting the mixture in a warm place to macerate for 1 hour. You can heat the mixture in a 200-degree oven for 30 minutes to speed up the process. Blend with a stick blender or pour into a food processor to puree, then strain. You'll have 2 to 2 1/2 cups of puree.
Step 2Stir 2 cups of the puree into the vanilla ice cream. Chill, ideally to 38 degrees, 2 to 3 hours or overnight. Process in an ice cream machine according to the manufacturer's directions.