01 - Place butter in a saucepan over medium heat. Melt, then continue to cook, swirling often, until butter foams and turns golden brown with a nutty aroma (about 5–7 minutes). Remove from heat and let cool for 10 minutes.
02 - In a large bowl, whisk together browned butter, brown sugar, and granulated sugar until combined. Add mashed banana, egg, and vanilla extract. Mix until smooth.
03 - In a separate bowl, whisk together flour, baking soda, and salt.
04 - Add dry ingredients to wet ingredients and mix until just combined.
05 - Fold in chocolate chips and nuts, if using.
06 - Cover dough and chill for at least 30 minutes (up to 2 hours) for thicker cookies.
07 - Preheat oven to 350°F. Line baking sheets with parchment paper.
08 - Scoop dough (about 2 tablespoons per cookie) onto prepared sheets, spacing 2 inches apart.
09 - Bake 10–12 minutes, or until edges are golden and centers are just set.
10 - Cool on baking sheets for 5 minutes, then transfer to a wire rack to cool completely.