Ingredients:
1 12-oz container frozen whipped topping, thawed
1 14-oz can sweetened condensed milk
1 8-oz package cream cheese, softened
2 cups milk
1 5.1-oz box instant French vanilla pudding mix
6 to 8 bananas, sliced
2 7.25-oz bags Pepperidge Farm Chessmen cookies
Instructions:
Line the bottom of a 3-quart 13×9 baking dish with a single layer of cookies.
Combine cream cheese and sweetened condensed milk in a large mixing bowl then beat with an electric mixer until smooth. Mix in regular milk until smooth.
Add pudding mix then continue mixing until well combined.
Add whipped topping to the mixture then fold together until incorporated.
Spoon a thin layer of pudding mixture over cookies (just enough to cover).
Arrange banana slices over pudding. Some overlapping is OK – they don’t have to lay flat.
Pour remaining pudding mixture over bananas then spread evenly.
Cover pudding mixture with remaining cookies. Cover and refrigerate 6 hours (or overnight) before serving.
Notes:
If you can’t find a large box of instant French vanilla pudding, use regular vanilla then add a teaspoon of vanilla extract when mixing to help get that stronger “French vanilla” flavor.
I haven’t been able to find the 12-oz containers of cool whip in a coon’s age so I just buy two of the 8-oz containers and use one and a half (I find this easier than guessing with the 16-oz container plus I use the 8-oz containers to pack my leftovers for lunch 
).
You won’t use quite all of the cookies. Since some of them break in the package, put all the broken ones in the bottom of the dish and save the good ones for the top.
The dessert will need to rest at least 6 hours before serving to ensure the cookies have time to soften.