Preheat your oven to 350°F (175°C). Grease an 8x8-inch baking dish.
In a mixing bowl, combine the flour, sugar, butter, baking powder, and salt. Mix until crumbly.
Add the egg and vanilla extract, and stir until well combined. Fold in the mashed bananas.
Spread the batter evenly into the prepared baking dish. Bake for 20-25 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool completely in the pan.
In another bowl, whisk together the instant pudding mix and milk until smooth. Let it sit for about 5 minutes to thicken.
Once the bars are cooled, spread the pudding mixture evenly over the top.
Top with whipped topping, then sprinkle crushed vanilla wafers and sliced bananas on top.
Refrigerate for at least 2 hours before serving to allow the flavors to meld.