Assemble the cheesecake strawberry ice cream. Evenly spread about ½ of the base cheesecake ice cream into a large freezer safe container. Swirl ½ of the cooled strawberry sauce into the base ice cream. Top the strawberry swirl with graham cracker crumbs and ½ of the remaining cup of cheesecake pieces. Repeat with the remaining cream cheese ice cream, followed by the strawberry sauce, graham cracker crumbs and cheesecake pieces.