Place the butter in a light-colored skillet or saucepan over medium heat. Cook, stirring or swirling frequently, until the butter foams and the milk solids on the bottom turn golden brown and smell nutty.
Immediately pour the browned butter into a large mixing bowl, scraping in all of the brown bits. Let it cool until it is no longer hot.
Add the dark brown sugar and granulated sugar. Mix until combined.
Add the pumpkin puree, egg yolk, and vanilla extract. Mix until smooth.
In a separate bowl, whisk together the flour, baking soda, cinnamon, pumpkin pie spice, and salt.
Add the dry ingredients to the wet ingredients and mix just until combined. The dough can be baked right away or chilled if desired.
Preheat the oven to 350°F. Prepare your baking sheets with parchment paper or silicone baking mats.
Stir together the ⅓ cup granulated sugar and 1 teaspoon cinnamon in a small bowl.
Portion the cookie dough into 3-ounce (85 g) balls.
Roll each dough ball in the cinnamon sugar until completely coated.
Place the cookies about 3 inches apart on the prepared baking sheet.
Bake for 18 minutes, until the edges are set but the centers still look soft. If you make smaller cookies, reduce the baking time accordingly.
Let the cookies cool on the baking sheet for 2 to 3 minutes, then transfer to a cooling rack.