Preheat your oven to 350°F (175°C) and grease a 9x9-inch baking pan or line it with parchment paper.
In a large mixing bowl, combine the mashed bananas and melted butter. Mix until well combined.
Add the granulated sugar, eggs, and vanilla extract to the banana mixture. Stir until smooth.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chopped walnuts and chocolate chips, if using.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the brownies to cool in the pan for about 10 minutes before transferring them to a wire rack to cool completely.