Start by preparing the browned butter by heating the butter in a saucepan over very low heat. Stir regularly until the butter turns a nice brown color and develops a nutty aroma. Be careful as this can happen quickly. Stop cooking as soon as it starts to brown and let it cool.

Mash the bananas with a fork in a mixing bowl.

Then, add the eggs, both sugars, baking soda, and salt, and mix vigorously again.

Add the cooled browned butter, mix again, then finally add the flour.

After adding the flour, do not overmix the batter to keep the cake moist: gently and briefly mix until just combined.

Finally, add the chocolate chips and nuts.

Pour this mixture into a tall loaf pan lined with parchment paper.

Preheat the oven to 180°C (350°F) and bake for about 50 minutes. Check doneness with a wooden skewer; when it comes out dry, the cake is done.