In a 13x9 dish pour the whole box of cookies into your pan and set aside.
In a medium size saucepan pour your 5 3/4 cups of milk and your two packages of pudding mix and cook on medium heat, stirring constantly until pudding thickens. Remove from burner and add vanilla.
Slice your bananas over the cookies, then pour your pudding over bananas. Add 2 teaspoons of vanilla to your whip topping and spread over your pudding layer and chill in the refrigerator for at least 2 hours