Brown the butter in a medium-sized saucepan over medium heat for about 5 minutes, swirling constantly until it foams and releases a nutty aroma. Remove from heat and let it cool.
Preheat your oven to 180°C (350°F). Line a loaf pan with parchment paper.
Mash your ripe bananas in a large mixing bowl until smooth.
Add the cooled brown butter, brown sugar, granulated sugar, salt, vanilla extract, cinnamon, and Greek yogurt to the bowl, mixing until well combined.
Whisk in the eggs until just combined, avoiding overmixing.
Gradually incorporate the flour and baking soda into the bowl, mixing until almost combined.
Fold in the chocolate chips gently to ensure they are evenly distributed throughout the batter.
Pour the batter into your prepared loaf pan and sprinkle extra chocolate chips on top.
Bake for 50-60 minutes, checking with a toothpick in the center; it should come out clean when done.
Allow the loaf to cool for at least 20 minutes before slicing and enjoying.