Preheat your oven to 350°F. Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy. Beat in the mashed bananas, egg, and vanilla extract until well combined.
In a separate bowl, mix together the rolled oats, all-purpose flour, baking soda, ground cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. If desired, fold in chopped nuts or chocolate chips.
Drop rounded tablespoons of cookie dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10-12 minutes or until the edges are golden brown. The centers may still be soft, but they will firm up as they cool.
Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.