Preheat the oven to 350°F (175°C). Grease and line a 9x13-inch baking dish with parchment paper.

In a large mixing bowl, cream together the melted butter and sugar until smooth. Add in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In another bowl, whisk together the flour and cocoa powder. Gradually add this mixture to the wet ingredients until fully combined.

Pour the brownie batter into the prepared baking dish, spreading it evenly. Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Allow the brownies to cool completely.

Mix the banana pudding mix with whole milk in a separate bowl. Whisk until smooth and lightly thickened.

Once the brownies have cooled, spread the banana pudding over the top. Then, spread the whipped topping evenly over the banana layer.

Sprinkle crushed Nilla wafers over the top of the whipped topping for a textured finish.

Place the brownies in the refrigerator for at least 2 hours before cutting into squares.