Line an 8x8-inch baking pan with parchment paper, leaving an overhang for easy removal. Set aside. Remove 1 heaping cup of whipped topping and set it aside.
In a large bowl, combine both pudding mixes and milk and briskly whisk together for about 1 minute or until smooth. Take the remaining whipped topping and gently fold it into the pudding mixture until completely incorporated.
Place cookies in the prepared pan, breaking them apart as needed to create an even layer. Top with half the pudding mixture and use the back of a large spoon to gently spread into an even layer. Top with more cookies. Add the rest of the pudding, again spreading it into an even layer. Add the last layer of cookies. Finally, spread the reserved whipped topping in an even layer. Cover the cake and refrigerate for 24 hours. (This cake takes a little longer than most icebox cakes for the cookies to soften because they’re so thick!)
When ready to serve, cut the cake into squares (see note 4) and, if desired, use a zester to grate a bit of lemon zest on top. Alternatively, crumble any leftover cookies on top. Enjoy slices cold, straight out of the fridge.
Notes
Note 1: Loorna Doone Shortbread Cookies are used as the base of the cake and provide a sweet, buttery flavor. They soften when layered with the pudding mixture, becoming a cake-like consistency. While I highly recommend using 2 boxes of them for this recipe, graham crackers or vanilla wafers can be used as a substitute.Note 2: Use 2 boxes of regular instant pudding mix (not sugar-free, low-fat, or the cook-and-serve type). Be sure to get the small 3.4-ounce boxes, and don’t prepare the pudding according to package instructions.Note 3: Cool Whip is a common brand of frozen whipped topping that I use in my tests. Be sure to use regular, not sugar-free/reduced-fat, which can become watery. Or make your own; my recipe for homemade whipped cream is in the blog post!Note 4: When cutting the cake, use a sharp chef’s knife and make decisive cuts. Run the knife under warm water, dry it on a kitchen towel, and repeat for each cut.Storage: I recommend eating the cake on days 2 or 3. It can become watery after that. Serve the cake directly from the fridge. Any leftovers should be returned to the fridge promptly. I do not recommend freezing.