Make brown sugar mixture: Preheat oven to 350°F. Coat a 13- x 9-inch baking pan with cooking spray. Vigorously whisk together brown sugar and 1 ½ cups of the melted butter in a large bowl until smooth. Whisk in banana, vanilla, and 2 of the eggs until combined.

Make batter: Whisk together flour, baking soda, 1 package of the pudding and pie filling, and ½ teaspoon of the salt in a medium bowl; add to sugar mixture, whisking until fully combined. (Batter will be very thick.)

Spread batter in pan: Transfer half (about 2 heaping cups) of batter to prepared baking pan. Using a silicone spatula, spread batter in an even layer, touching all edges of baking pan.

Make cream cheese filling: Beat cream cheese with a stand mixer fitted with a paddle attachment on medium speed until smooth, 1 to 2 minutes, stopping to scrape down sides of bowl as needed.

Reduce mixer speed to low; add remaining 3 eggs, 1 at a time, beating until just combined after each addition and stopping to scrape sides of bowl as needed. Add remaining 1 package pudding and pie filling and ¼ teaspoon salt; increase mixer speed to medium, and beat until combined and smooth, about 2 minutes.

Add cream cheese mixture to pan: Spread cream cheese mixture over batter in baking pan in an even layer.

Add top layer of batter: Scoop remaining batter evenly over cream cheese mixture; using hands or an offset spatula, gently spread and press into an even layer, covering most of cream cheese layer.

Sprinkle vanilla wafers: Stir together vanilla wafers and remaining 1 tablespoon butter in a bowl. Sprinkle evenly over top of batter.

Bake: Bake in preheated oven until set, 35 to 40 minutes. Remove from oven; transfer to a wire rack, and let cool completely, about 2 hours.