Bring cream and milk to simmer in heavy medium saucepan. Whisk yolks and sugar in a large bowl to blend. Gradually whisk in hot cream mixture. Return to saucepan; stir over medium-low heat until custard thickens and leaves path on back of spoon when finger is drawn across, about 5 minutes (do not boil). Strain into medium bowl. Chill until cold. Whisk in the berry puree. Process in ice cream maker according to manufacturer’s instructions. Transfer to covered container and freeze.

Can be made 1 week ahead. Keep frozen.