Make the Pudding Base: In a large bowl, whisk sweetened condensed milk with cold water until smooth. Add the pudding mix and beat for 2 minutes until thickened. Chill for 5 minutes.
Prepare the Cream Layer: In another bowl, beat the softened cream cheese until smooth. Gently fold in the whipped topping or whipped cream until light and fluffy.
Combine Layers: Mix the chilled pudding into the cream cheese mixture. Stir gently until fully incorporated and smooth.
Layer the Dish: Line the bottom of a 9x13 glass dish with a layer of Chessmen cookies. Add sliced bananas evenly on top of the cookies.
Add Creamy Mixture: Spread the pudding-cream mixture over the banana and cookie layer.
Top It Off: Add a final layer of Chessmen cookies on top. Cover and refrigerate for at least 4 hours or overnight for best flavor and texture.
