**Layer the Cookies and Bananas**
- Line the bottom of a 9x13-inch baking dish with one bag of Chessmen cookies. Arrange the sliced bananas evenly over the cookies.
**Make the Cream Mixture**
- In a large mixing bowl, use a hand mixer to beat the softened cream cheese until smooth. Add the sweetened condensed milk and mix until fully combined.
**Prepare the Pudding**
- In a separate bowl, whisk together the instant pudding mix and cold milk until thickened, about 2 minutes. Fold the pudding into the cream cheese mixture until smooth.
**Add the Whipped Topping**
- Gently fold the whipped topping into the pudding mixture until no streaks remain.
**Assemble the Pudding**
- Pour the cream mixture over the banana layer, spreading evenly. Top with the second bag of Chessmen cookies to create a decorative layer.
**Chill and Serve**
- Cover the dish with plastic wrap and refrigerate for at least 4 hours, or overnight, to allow the flavors to meld. Serve cold and enjoy!