Set your oven to heat up to 350°F. Grab a 9x13-inch baking dish and completely line its interior with parchment paper.
Take a mixing bowl and, utilizing an electric hand mixer or a stand mixer, whip the melted sweet cream butter alongside both the granulated and soft brown sugars until the mixture appears wonderfully light and fluffy. Next, blend in the large eggs and pure vanilla essence until perfectly smooth.
Grab a separate bowl and toss together the unbleached plain flour, the unsweetened cocoa powder, and the fine table salt. Incorporate these dry components into your wet batter in three separate batches, delicately folding until the mixture just comes together.
Stir the half-sweet chocolate morsels into the mixture. Scrape every bit out and level this dense, fudgy base entirely across your lined baking dish.
Whip the room-temperature cream cheese in a fresh bowl until it's completely lump-free. Pour in the quick-set pudding powder along with the regular dairy milk, beating repeatedly until seamlessly integrated. Grab a silicone spatula to carefully fold in your diced fresh banana bits.
Dollop and spread this fruity cream cheese layer evenly across the raw chocolate batter below. Scatter your crunchy vanilla wafer chunks generously covering the topmost surface.
Place the dish onto the middle oven rack and bake, uncovered, for about 30 to 40 minutes. You will know it is ready once the outer pudding edges take on a beautiful golden hue and the very center is firm enough to not slosh when gently moved.
Permit the baking pan to cool down to room temperature entirely before utilizing a sharp knife to portion it out into thick squares. Avoid rushing this cooling phase for the absolute cleanest slices!