In a saucepan over medium heat, melt the butter, stirring frequently until it turns golden brown and has a nutty aroma. Remove from heat and let cool slightly.

In a mixing bowl, combine the brown butter, pumpkin puree, brown sugar, maple syrup, egg, and vanilla extract. Whisk until smooth.

In another bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in chocolate chips and walnuts if using.

Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper. Drop tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake for 10-12 minutes or until the edges are set and the centers look slightly underbaked. Let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.