In a loaf pan, spread a fourth of the vanilla ice cream on the bottom of the pan. Place 3 ice cream sandwiches on top of the ice cream layer, and cut the sandwiches as needed to fit. Spread half of the remaining ice cream over the sandwiches.
Evenly crumble the cookie dough over the ice cream layer and press the dough gently into the ice cream. Layer the remaining ice cream sandwiches over the cookie dough and spread the remaining ice cream over the top. Transfer the pan to the freezer for a minimum of 6 hours.
Remove the ice cream cake from the freezer and place it in a warm water bath for no more than a minute. Invert the cake onto a plate and remove the pan. Place the cake back into the freezer for 1 hour.
In a bowl, combine the Cool Whip Frosting and Topping; mix until combined. Remove the cake from the freezer and frost the cake with a third of the Cool Whip mixture. Place the cake back into the freezer for 30 minutes.
Frost the cake with the remaining Cool Whip mixture, and top with chocolate sprinkles, if using. Place the cake in the freezer for another 30 minutes before serving.
Notes
For best results, freeze the cake overnight before serving.