In a large bowl, combine half of the pudding and the whipped cream. Fold together with a spatula until well combined. Set the other half of the pudding aside.
In a deep, rectangular serving dish, cover the bottom with one layer of chessmen cookies (one sleeve should be enough).
Use the remaining half of the pudding to cover the layer of cookies evenly and smooth out.
Slice two bananas very thin and cover the pudding with an even layer of banana slices.
Use another sleeve of chessmen cookies to create the next layer. You can alternate the direction of the rows of cookies you want.
Top the cookies with an even layer of the pudding/whipped cream mixture. Spread evenly to cover all of the cookies.
Slice two bananas very thin and cover the pudding with an even layer of banana slices.
In a food processor, grind the remaining sleeve of chessmen cookies until they turn into fine crumbs. Spread the crumbs on top of the banana slices and then smooth with the back of a spoon so the cookie crumbs are packed in nicely. The surface should be a smooth layer of cookie crumbs.