Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add the mashed bananas, egg, and vanilla extract to the mixture, and mix until well combined.
In a separate bowl, whisk together the baking soda, salt, and flour. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
If desired, fold in the chopped walnuts and chocolate chips.
Drop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.