Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper.

In a medium saucepan, melt the butter over medium heat. Continue cooking, stirring frequently, until the butter turns golden brown and has a nutty aroma. Remove from heat and let it cool slightly.

In a large mixing bowl, combine the mashed bananas, browned butter, granulated sugar, and brown sugar. Mix well until smooth.

Add the eggs and vanilla extract to the banana mixture, stirring until fully incorporated.

In a separate bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.

If using, fold in the chopped nuts.

Pour the batter into the prepared loaf pan and smooth the top with a spatula.

Bake for 60-65 minutes, or until a toothpick inserted into the center comes out clean.

Allow the bread to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.