Preheat the oven to 350°F (175°C) and grease an 8x8 inch square baking pan or line with parchment paper.

In a large mixing bowl, combine the melted butter and granulated sugar, whisking until smooth.

Whisk in the egg, vanilla extract, and mashed banana until fully incorporated.

Add the dry instant vanilla pudding mix and stir until the color is uniform and the powder is dissolved.

Gradually fold in the flour and salt using a spatula until just combined.

Fold in the white chocolate chips.

Spread the batter evenly into the prepared baking pan.

Arrange the vanilla wafer cookies in a grid pattern on top of the batter, pressing them down lightly.

Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean or with only a few moist crumbs.

Allow the brownies to cool completely in the pan for at least 1 hour before slicing to ensure the pudding-set texture is maintained.