Preheat oven to 375. Spray a 13x9 baking dish with cooking spray.
In a medium bowl cut butter into cookie mix until mixture is crumbly. Reserve 3/4 cup of mixture for topping. Mix egg in remaining cookie mixture until incorporated. Press crumbs evenly in bottom of baking dish. Bake 13 to 15 minutes or until light golden brown around the edges. Cool completely.
On a cookie sheet place the reserved topping crumbs in a thin layer. Bake 8 minutes stirring occasionally or until light golden brown. Crumble into small pieces.
In a large mixing bowl beat cream cheese with electric mixer until smooth, add sweetened condensed milk, beat until well blended. Beat in the whipped topping until smooth. Add the pudding mix and continue to beat for an additional 2 minutes or until everthing is combined and fluffy.
Spread 1/3 of pudding mixture onto the cooled cookie base. arrange bananas in a single layer of pudding mix. Top with remaining pudding mixture and refrigerate for 10 minutes or until set. Sprinkle the reserved cookie crumbs over the pudding.