Place a cookie sheet in the freezer and chill completely.
Turn your chilled cookie sheet upside down and lay four ice cream sandwiches on the sheet to form a large rectangle.
Place scoops of the softened ice cream along the length of the sandwiches to cover them completely. “Sandwich” the ice cream scoops between the remaining four ice cream sandwiches, laying them down on top like the bottom layer. Return the log to the freezer to firm up for about 2 hours.