Preheat your oven to 350°F (175°C). Grease the 8x8-inch baking pan or line it with parchment paper.
In a large mixing bowl, mash the ripe bananas using a fork or potato masher until smooth.
Add the melted butter to the mashed bananas and mix well.
Stir in the brown sugar until fully combined.
Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
In another bowl, whisk together the flour, baking soda, salt, and cocoa powder until well combined.
Gradually fold the dry ingredients into the wet ingredients until just combined. Be careful not to overmix.
If desired, fold in the chocolate chips.
Pour the brownie batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 20-25 minutes or until a toothpick inserted into the center comes out with a few moist crumbs.
Once baked, allow the brownies to cool in the pan for about 10 minutes before transferring them to a wire rack to cool completely.
Cut into 12 squares and serve.