In a mixing bowl, stir together the softened cream cheese, and cocoa powder. Slowly add sugar and milk alternately, scraping sides of bowl to make a thin paste.
Add vanilla. Using a handheld electric mixer, beat until smooth. Fold in about half a carton (1 ¾ cups) of the whipped topping. Fold in the cookies.
Lay a large sheet of foil on a flat surface.
Lay 4 ice cream sandwiches side by side on the foil.
Spread half of the chocolate mixture over the sandwiches.
Layer 4 more ice cream sandwiches over the chocolate mixture, then layer on remaining chocolate mixture and 4 ice cream sandwiches.Using some or all of the remaining carton of whipped topping, spread a thin layer all over the cake. At this point it will look pretty shoddy, but that’s okay. You’ll fix it later. Bring foil up and around cake to make a little container, then set the cake in a pan (just to keep it level) and put it all in the freezer for about 6 hours or until frozen solid. When frozen, remove foil and spread more whipped topping over the cake. Arrange on a nice plate and touch up your whipped topping.
Garnish with chocolate syrup or cookie crumbs and slice.
