Preheat oven to 425 degrees.
In a large mixing bowl, microwave butter until melted (about 20 seconds). Add banana to the bowl and mash with a fork. Next add eggs, brown sugar, and vanilla and mix until well combined.
Add flour, baking soda, salt, and cocoa powder and mix until all the flour is incorporated. Add 1/3 cup of chocolate chips, and mix.
Line a standard muffin tin with silicone or paper liners. Fill muffin tin liners 3/4ths of the way full. Divide the remaining chocolate chips on top of the muffins.
Bake muffins for 8 minutes. Then, reduce the oven temperature to 350 degrees, and continue baking for an additional 6-9 minutes. Muffins will be done when a toothpick inserted in the middle of the muffin comes out with just a few crumbs sticking to the toothpick.
Allow muffins to cool in the pan for 5-10 minutes. Then, remove and enjoy!