In a large mixing bowl, combine the vanilla pudding mix and cold milk. Whisk until smooth.
Add the sweetened condensed milk and vanilla extract to the pudding mixture. Stir until well blended.
Fold in the whipped topping gently until fully incorporated.
In a large serving dish, layer the vanilla wafers on the bottom.
Add a layer of sliced bananas on top of the wafers.
Pour a layer of the pudding mixture over the bananas.
Repeat the layering process: wafers, bananas, and pudding until all ingredients are used.
Finish with a layer of whipped topping on top.
Chill the banana pudding in the refrigerator for at least 4 hours, or overnight if possible.
Serve cold, garnished with additional banana slices and wafers if desired.