Preheat your oven to 350°F and coat a 13x9-inch baking pan with cooking spray.
In a large bowl, whisk together brown sugar and 1 ½ cups melted butter until smooth. Stir in mashed banana, vanilla, and 2 eggs until combined.
In a medium bowl, whisk together flour, baking soda, 1 package of banana pudding mix, and ½ teaspoon salt. Gradually add this to the sugar mixture, whisking until fully combined. The batter will be thick.
Transfer half of the batter to the prepared baking pan, spreading it evenly to cover the bottom.
In a stand mixer, beat the cream cheese on medium speed until smooth. Reduce the speed and add the remaining 3 eggs one at a time. Add the remaining pudding mix and ¼ teaspoon salt, then beat until smooth.
Spread the cream cheese mixture over the batter in the pan in an even layer.
Gently scoop the remaining batter over the cream cheese layer, pressing it to cover most of the cream cheese.
Stir together crushed vanilla wafers and the remaining tablespoon of melted butter, then sprinkle evenly on top of the batter.
Bake for 35-40 minutes, until set. Let the dessert cool completely for about 2 hours on a wire rack before serving.