Melt the butter, then let it cool (this is important, otherwise it will cook your eggs when you mix them together).
In a large bowl, whisk the eggs with the brown sugar and a packet of intense vanilla sugar until the mixture turns white and becomes frothy. Then pour in the melted butter and mix again.
In a second bowl, combine the dry ingredients: flour, baking powder, salt, and baking soda. Add this mixture to the previous mixture in several batches, mixing well to avoid lumps.
Mash the ripe bananas with a fork, then stir them into the batter.
Add the chocolate chunks to your mixture.
Grease a cake pan and pour in the mixture. Sprinkle vanilla sugar on top.
Bake for 45 to 50 minutes at 350°F. Check to see if it’s done by inserting a knife blade: it should come out dry.