Start by choosing a 13x9 baking dish or casserole dish. Line the bottom with one full layer of Chessmen cookies, using any broken pieces on the bottom since they will be covered. Add a full layer of sliced bananas over the cookies and spread them out evenly.
In a large mixing bowl, combine the milk and instant French vanilla pudding mix. Use an electric mixer and beat for several minutes until the mixture starts to thicken. This gives the dessert its base and helps everything set properly after chilling.
In a separate bowl, beat the softened cream cheese and sweetened condensed milk together until smooth. Take your time on this part because it helps prevent lumps and gives the pudding mixture a rich, creamy finish.
Once the cream cheese mixture is smooth, gently fold in the thawed whipped topping. Mix just until combined so the filling stays light and fluffy instead of getting dense.
Add the cream cheese mixture into the prepared pudding mixture and stir or mix until everything is fully blended. The finished filling should be smooth, thick, and easy to spread.
Pour the pudding mixture over the cookie and banana layers in the pan. Spread it gently all the way to the edges so every bite has an even balance of filling, fruit, and cookies.
Arrange the remaining Chessmen cookies across the top of the pudding mixture. Try to use the best-looking cookies here since they will be visible when serving.
Cover the dish carefully with plastic wrap and refrigerate for at least 4 hours before serving. For the best texture, let it chill overnight so the flavors can settle and the cookies soften just enough.