Triple-Chocolate Cookie And Strawberry Ice Cream Sandwiches

Combine strawberries, 1/3 cup sugar, and corn syrup in medium bowl. Using potato masher, mash until puree forms; let stand 30 minutes.
Meanwhile, bring cream, milk, and remaining 1/4 cup sugar to simmer in heavy medium saucepan, stirring until sugar dissolves. Remove from heat. Using electric mixer, beat yolks in medium bowl until thick and pale yellow, about 3 minutes. Gradually beat in hot cream mixture. Return mixture to saucepan. Stir over medium heat until custard thickens and forms path on back of spoon when finger is drawn across, about 4 minutes (do not boil). Strain custard into large bowl. Cool. Stir in strawberry mixture and vanilla. Cover and refrigerate custard until cold, at least 3 hours and up to 1 day.
Process custard in ice cream maker according to manufacturer's instructions. Transfer ice cream to container; cover and freeze until firm, at least 6 hours. (Can be prepared 3 days ahead. Keep frozen.)
Place 1 frozen Triple-Chocolate Cookie flat side up on work surface. Place 1/2 cup ice cream atop cookie. Using offset spatula or butter knife, gently spread ice cream to cover cookie; top with another cookie, flat side down, and press gently to adhere. Repeat with remaining ice cream and cookies, making 8 ice cream sandwiches total. Wrap and freeze until firm, at least 4 hours or overnight. Let ice cream sandwiches stand at room temperature 5 minutes before serving.