Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper if desired.
In a mixing bowl, combine the mashed bananas and softened butter. Mix until smooth and well combined.
Add the brown sugar and granulated sugar to the banana mixture, and mix until creamy.
Beat in the egg and vanilla extract until fully incorporated.
In another bowl, whisk together the baking soda, salt, and all-purpose flour.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
If desired, fold in chocolate chips and/or chopped nuts for added texture and flavor.
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden.
Remove from the oven and let the cookies cool on the baking sheet for a few minutes before transferring them to a cooling rack.