Preheat oven to 350°F. Move rack to lower-middle position. Generously grease a 9 x 5 inch loaf pan.
Beat bananas with an electric mixer until smooth. Add brown sugar, butter, and eggs, and mix until completely incorporated.
In a separate bowl, whisk together flour, baking soda, baking powder, and salt. Add dry ingredients to the wet ingredients, and beat until smooth, scraping down the sides and bottom of the bowl as needed.
Stir in the walnuts and/or chocolate chips, if you're using them.
Pour batter into prepared pan, and bake for one hour, or until bread is a deep brown and an inserted skewer comes out clean.