In a saucepan over medium heat, melt the butter and continue cooking until it turns golden brown and has a nutty aroma, about 5-7 minutes. Remove from heat and let cool slightly.

In a large 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, 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 but the centers are still soft. Let cool on the baking sheet for 5 minutes before transferring to a wire rack.