In a small saucepan, melt the butter over medium heat. Let it bubble and foam, swirling occasionally. Keep cooking until the milk solids turn a nutty brown color and the aroma is distinctively rich, about 5 to 7 minutes. Immediately transfer the butter to a heatproof bowl or the stand mixer bowl to stop the cooking process.

To the brown butter, add the granulated sugar and the brown sugar. Beat until light and fluffy, scraping down the sides.

Beat in the room temperature egg and vanilla until just combined. Then, gently fold in the mashed, ripe bananas. Mix only until streaks of banana are gone.

In a separate bowl, whisk together the flour, baking soda, salt, and cinnamon.

Gradually add the dry mixture to the wet mixture, mixing on low speed until just combined. If using, fold in the chocolate chips or nuts.

Cover the bowl and chill the dough for at least 30 minutes, or up to 2 hours.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper. Use a cookie scoop (about 2 tablespoons) to drop the dough onto the sheets, spacing them about 2 inches apart. For a cinnamon sugar top, roll the tops in extra cinnamon sugar.

Bake for 10 to 12 minutes. The cookies will look slightly soft, and the edges will be set and lightly golden.

Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.