For the Cookies

1. Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
2. In a large bowl, cream together butter, white sugar, and brown sugar until smooth.
3. Mix in pumpkin puree and egg until fully combined.
4. In a separate bowl, whisk together flour, baking soda, cinnamon, nutmeg, cloves, and salt.
5. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
6. If using, fold in chopped walnuts.
7. Drop rounded tablespoons of dough onto the prepared baking sheets.
8. Bake for 15 to 20 minutes, or until the edges are lightly golden.
9. Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack.

For the Brown Butter Icing

1. In a saucepan, melt butter over medium heat, stirring constantly until it turns golden brown and smells nutty.
2. Remove from heat and whisk in powdered sugar, vanilla extract, and milk until smooth.
3. Drizzle the warm icing over cooled cookies.
4. Allow icing to set before serving