Preheat the oven to 350°F (175°C) and lightly grease or butter the sides of a 9x13 glass baking dish.

In a medium bowl, whisk the flour with the baking powder, salt, and cocoa.

In a standing electric mixer, beat 2 sticks of butter with the granulated sugar at medium speed until very fluffy, about 5 minutes.

Beat in the eggs one at a time.

Add the vanilla and mix.

Beat in the flour mixture and the milk until well combined.

In a small bowl, blend the remaining stick of butter with the brown sugar and spread it evenly in the baking dish.

Arrange the bananas, cut sides down, in the dish and spoon dollops of the peanut butter over the bananas.

Fill in the gaps with the chocolate batter.

Bake in the preheated oven for 45 minutes.

Let the cake cool for 10 minutes, then loosen the edges with a knife and invert it onto a platter.

Let the cake cool slightly, then cut into squares and serve.