Brown the butter by melting it in a saucepan over medium heat until golden brown, about 5-7 minutes. Let cool for 10 minutes.

Mix the cooled browned butter, brown sugar, granulated sugar, and egg in a large bowl until smooth. Stir in vanilla extract and mashed bananas until well combined.

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

Gradually mix dry ingredients into wet ingredients until just combined. Fold in chopped walnuts if using.

Chill the dough in the refrigerator for 20-30 minutes for best results.

Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper. Drop tablespoons of dough on the sheets, leaving space between each.

Bake for 10 minutes until the edges are golden but the centers are soft.

Cool cookies on the pan for 5 minutes before transferring to a wire rack.

Prepare the cinnamon drizzle by whisking powdered sugar, ground cinnamon, and milk in a small bowl until smooth. Drizzle over cooled cookies.