Preheat oven to 350°F (175°C). Lightly grease or butter the sides of a 9×13-inch glass baking dish.
In a medium bowl, whisk together 1 1/2 cups all-purpose flour, 1 1/2 cups whole wheat pastry flour, 1 tablespoon baking powder, 1/2 teaspoon salt, and 1/3 cup cocoa.
In a large bowl, whisk 2 large eggs and 1 cup sugar until smooth. Add 1 cup milk and 1/2 cup melted coconut oil and whisk until combined.
Stir 3 mashed ripe bananas and 2 teaspoons vanilla extract into the wet mixture until mixed.
Gradually add the dry ingredients to the wet mixture and stir until just combined. Fold in 1 cup chocolate chips.
In a small bowl, blend 4 tablespoons butter with 1/4 cup brown sugar until combined. Spread this butter–sugar mixture evenly in the bottom of the prepared baking dish.
Arrange the 1 sliced banana in a single layer over the butter–sugar mixture.
Drop spoonfuls of the 3/4 cup chunky peanut butter over the banana layer, distributing the dollops evenly.
Spoon the chocolate banana cake batter over the banana and peanut butter layer, filling the dish and smoothing the top as needed.
Bake for 45–55 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs. Remove from oven and let cool in the pan for 10 minutes.
Run a knife around the edges to loosen, then invert the cake onto a platter. Let the inverted cake cool slightly while you make the sauce.
In a microwave-safe bowl combine the remaining 4 tablespoons butter, remaining 1/4 cup brown sugar, 2 tablespoons creamy peanut butter, and 1 teaspoon vanilla extract. Microwave in 30-second intervals, stirring after each, for a total of about 1 minute, until smooth and melted.
Pour the warm peanut butter caramel sauce over the cake, let it set slightly, then cut into squares and serve.