Step 1: Preheat your oven to 350°F (175°C) and grease a 9x5 inch loaf pan with butter or non-stick spray.
Step 2: In a small saucepan, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter turns a golden brown color and smells nutty. Remove from heat and let cool for 5 minutes.
Step 3: In a large mixing bowl, mash the overripe bananas until smooth. Add the browned butter (including the brown bits from the bottom of the pan) and stir until combined.
Step 4: Whisk in the brown sugar, egg, and vanilla extract until the mixture is smooth and well incorporated.
Step 5: Sprinkle the baking soda, salt, and cinnamon over the wet ingredients and stir well.
Step 6: Gently fold in the flour using a spatula. Mix until just combined, being careful not to over-mix the batter. If using walnuts or chocolate chips, fold them in now.
Step 7: Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Step 8: Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean.
Step 9: Remove from the oven and let the bread cool in the pan for 10 minutes before transferring to a wire rack to cool completely.