In a medium-sized bowl, pour in the cold whole milk and sprinkle in the instant French vanilla pudding powder. Use a hand mixer set to low speed to blend the two until the pudding becomes thick and fully combined, about 2 minutes. Set aside.

In a separate, larger bowl, add the softened cream cheese and pour in the sweetened condensed milk. Beat the mixture on low speed with the mixer until it becomes silky and lump-free.

Add the thawed whipped topping to the cream cheese mixture. Using a rubber spatula, fold it in gently until the mixture is uniform and airy. Avoid overmixing to preserve the whipped texture.

Pour the previously prepared pudding into the cream cheese mixture. Gently fold the two together with the spatula until no streaks remain.

Arrange one package of the butter cookies evenly along the bottom of a 9x13-inch baking dish.

Distribute the banana slices in a single layer over the cookies, covering the entire surface.

Spoon the pudding mixture over the banana layer, spreading it out to create a smooth top.

Place the second package of cookies across the surface of the pudding layer, decorative side facing up.

Cover the dessert tightly with plastic wrap and refrigerate for a minimum of 2 to 3 hours, allowing the pudding to set. For optimal texture and flavor, chilling overnight is recommended.

Serve chilled by scooping through all the layers down to the cookie base. Portion onto plates and enjoy immediately.