Preheat the oven to 350°F (175°C) and grease a loaf pan.

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

In a mixing bowl, combine the mashed bananas, granulated sugar, beaten eggs, and vanilla extract. Mix well.

Add the browned butter to the banana mixture and stir until combined.

In another bowl, whisk together the flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.

Pour the batter into the prepared loaf pan and smooth the top.

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

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