In a large mixing bowl, combine the sweetened condensed milk, instant vanilla pudding mix, and cold milk. Whisk for about 2 minutes, until smooth and slightly thickened, like loose custard. Place in the refrigerator to chill while you prepare the cream cheese.
1 can (14 oz) sweetened condensed milk, 1 box (5 oz) instant vanilla pudding mix, 2 cups cold milk
In another large bowl, beat the softened cream cheese with a hand mixer or stand mixer until completely smooth and fluffy, with no lumps. If using, beat in the vanilla extract and a small pinch of salt until well combined.
1 package (8 oz) cream cheese, 1/2 teaspoon vanilla extract, pinch salt
Remove the pudding mixture from the fridge. Add a spoonful or two of the pudding to the cream cheese and beat to loosen the cream cheese. Then pour in the remaining pudding mixture and beat until fully blended and silky, scraping down the sides and bottom of the bowl to ensure there are no cream cheese lumps.
1 can (14 oz) sweetened condensed milk, 1 box (5 oz) instant vanilla pudding mix, 2 cups cold milk, 1 package (8 oz) cream cheese
Using a spatula, gently fold the thawed whipped topping into the pudding and cream cheese mixture. Use broad, gentle strokes and rotate the bowl as you go, stopping when the mixture is mostly uniform and light. Avoid overmixing so you don’t deflate the filling.
1 container (12 oz) frozen whipped topping
In a 9×13-inch dish (glass looks especially nice), arrange one full, even layer of Chessmen cookies across the bottom, covering as much surface as possible. If using vanilla wafers, line them up in a snug single layer.
2 bags Pepperidge Farm Chessmen cookies
Slice the bananas just before assembling so they stay fresh-looking longer. Arrange a generous layer of banana slices over the cookies, using a single or double layer depending on how banana-forward you want the dessert.
6-8 medium ripe bananas
Pour the pudding and cream cheese mixture over the sliced bananas. Use a spatula to spread it evenly from edge to edge, ensuring all banana slices are completely covered to help prevent browning and keep the texture soft.
1 can (14 oz) sweetened condensed milk, 1 box (5 oz) instant vanilla pudding mix, 2 cups cold milk, 1 package (8 oz) cream cheese, 1 container (12 oz) frozen whipped topping, 6-8 medium ripe bananas
Arrange the second bag of Chessmen cookies in neat rows over the top of the filling, covering the surface. If some cookies crack, simply fit the pieces together; it will still look and taste great.
2 bags Pepperidge Farm Chessmen cookies
Cover the dish tightly with plastic wrap or a lid and refrigerate for at least 4 hours, or overnight for best flavor and texture. During this time, the cookies soften slightly and the layers meld together into a creamy, sliceable pudding.
Just before serving, optionally sprinkle lightly with ground cinnamon or nutmeg, or garnish with a few freshly sliced banana rounds. Slice into squares or scoop with a large spoon and serve chilled.
6-8 medium ripe bananas, ground cinnamon or nutmeg