Preheat the oven to 350°F (175°C) and grease a 9x13 inch baking pan.

In a mixing bowl, combine mashed bananas, granulated sugar, brown sugar, and melted butter. Mix well.

Add eggs and vanilla extract, and mix until combined.

In a separate bowl, whisk together flour, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in chocolate chips if using.

Pour the batter into the prepared baking pan and spread evenly.

Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.

Allow to cool completely in the pan.

In a saucepan, melt the butter over medium heat. Continue to cook until it turns golden brown and has a nutty aroma.

Remove from heat and let cool slightly.

In a mixing bowl, combine the browned butter, powdered sugar, milk, and vanilla extract. Beat until smooth and creamy.

Spread the frosting over the cooled brownies.