Preheat oven to 350 degrees.
In a large bowl, whisk melted butter and 2/3 cup brown sugar until well combined.
Add eggs, mashed bananas, and vanilla and whisk until blended in well.
In a separate bowl, combine flour and baking soda.
Add dry ingredients to wet ingredients.
Stir batter well so that no streaks of flour remain.
Grease 9x9 baking pan and add batter to pan.
Smooth into an even layer then sprinkle the top with the remaining brown sugar.
Bake for 20-25 minutes. The bread is done when a toothpick inserted into the center comes out clean.