Preheat your oven to 350°F (175°C) and adjust the rack to the center position.
In a medium saucepan, melt the unsalted butter over medium-low heat until it turns golden brown and develops a nutty aroma. Remove from heat and let cool.
Grease a 9×5-inch loaf pan or line it with parchment paper.
In a large bowl, mash the overripe bananas with a fork until smooth.
Add the cooled brown butter, brown sugar, egg, and vanilla extract to the mashed bananas and whisk until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Pour the dry ingredients into the bowl with the wet ingredients and gently fold until just combined.
Fold in the chocolate chips until evenly distributed.
Pour the batter into the prepared loaf pan and spread it out evenly.
Bake for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely before slicing.
