In a medium bowl, combine graham cracker crumbs and melted butter until well-coated. Press into the bottom of a 9x13-inch baking dish and refrigerate for about 15 minutes.

In a large bowl, beat softened cream cheese until smooth. Gradually add powdered sugar and vanilla, then fold in whipped topping. Spread over the crust.

Peel and slice bananas into ¼-inch rounds, layering them over the cream cheese mixture.

In a separate bowl, whisk together pudding mix and cold milk until thick, then spread over the banana layer.

Spread remaining whipped topping over the pudding layer and smooth for presentation.

Cover tightly and refrigerate for at least 4 hours or overnight.

Before serving, slice extra bananas and sprinkle on top with crushed graham crackers.