Preheat the oven to 180°C (356°F).
Mash the banana.
In a bowl, mix together the eggs, mashed banana, sugar, and melted butter.
Sift in cake flour, baking powder, and salt, then mix until combined.
Gently fold in the blueberries.
Pour the batter into a pan lined with parchment paper.
Bake in the oven at 180°C (356°F) for 35–40 minutes.
Let the finished cake cool before serving.