Preheat your oven to 350°F (175°C). Grease the 9x9 inch baking pan or line it with parchment paper.
In a mixing bowl, mash the ripe bananas until smooth. Stir in the melted butter until well mixed.
Add the granulated sugar, eggs, and vanilla extract to the banana mixture. Mix thoroughly until combined.
In a separate bowl, combine the all-purpose flour, cocoa powder, baking soda, and salt. Gradually fold the dry ingredients into the banana mixture until just combined. Do not overmix. If using, gently fold in the chocolate chips.
Pour the batter into the prepared baking pan and spread it evenly. Bake in the preheated oven for 25 minutes, or until a toothpick inserted into the center comes out clean.
While the brownies are baking, prepare the glaze. In a saucepan over low heat, whisk together the powdered sugar, milk, and vanilla extract until smooth. Remove from heat and set aside.
Once the brownies are done baking, allow them to cool in the pan for about 10 minutes. Then, transfer to a wire rack to finish cooling completely.
Once cooled, drizzle or spread the glaze over the brownies. Cut into squares and serve.