In a large mixing bowl, whisk together the cold milk and pudding mix until smooth. Set in the refrigerator for 30 minutes to chill.
In a large bowl using a hand mixer, beat the sweet condensed milk, cream cheese and vanilla extract on medium speed until well combined. Switch to a spatula and fold in the cool whip until fully incorporated. Gently fold the cream cheese mixture into the prepared pudding, ensuring a smooth and uniform consistency.
Spread one-third of the whole vanilla wafers in the bottom of a 9 × 13-inch baking dish. Sprinkle with half of the crushed cookies. Evenly spread one-third of the pudding mixture over the cookies. Layer half of the banana slices over the pudding mixture, then half of the remaining whole vanilla wafers.
Repeat with half of the remaining pudding, then the remaining bananas, and the remaining crushed cookies. Finish with the remaining pudding on the top. Cover with plastic wrap and refrigerate overnight to let the flavors set.
Before serving, decorate your banana pudding with whole wafers or Chessman cookies and/or with caramel sauce, as desired.
