In a medium-sized heavy saucepan, bring cream, milk, and strawberry puree to a boil.
Meanwhile, in a large bowl, whip egg yolks with a whisk. Gradually whisk in sugar until thoroughly combined. Slowly whisk the hot cream mixture into the egg yolks and return to saucepan. Over low heat, stirring constantly with a wooden spoon, cook until mixture heavily coats the back of the spoon. Return to bowl and cool over ice cubes and cold water.
Strain into a clean bowl and freeze in an ice-cream maker according to the manufacturer's directions. Scrape into a large container and freeze, covered, until needed.