Preheat the oven to 180°C (356°F).
Mash the banana and set aside.
Melt the dark chocolate and butter together in a double boiler.
Add eggs and sugar to a bowl and mix well.
Add the melted chocolate, butter, and mashed banana to the egg mixture and mix.
Sift flour and cocoa powder into the mixture and gently fold.
Pour the batter into a brownie pan.
Bake in the preheated oven for 25–30 minutes.
Cool before serving.