Finely chop the banana.
Whisk the eggs and sugar together.
Add melted butter and vanilla extract, then mix.
Sift cake flour, almond flour, baking powder, and cocoa powder into the batter and mix well.
Fold in the chopped banana and chocolate chips until evenly combined.
Pour the batter into madeleine molds.
Bake in a preheated oven at 170°C for 12–15 minutes.
Let cool, then remove from the molds.