Preheat the oven to 350°F (175°C). Grease the 9x9 inch baking pan or line it with parchment paper for easy removal.
In a mixing bowl, combine the melted butter and sugars (both brown and granulated) and whisk until smooth.
Add the mashed bananas and vanilla extract, stirring until well combined.
Beat in the eggs one at a time, ensuring each egg is well incorporated before adding the next.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, folding gently until fully combined. Be careful not to overmix.
If desired, fold in the chocolate chips.
Pour the batter into the prepared baking pan, smoothing it evenly with a spatula.
Bake in the preheated oven for 25 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Allow to cool in the pan for about 10 minutes before removing and transferring to a wire rack to cool completely. Cut into squares and serve.