Preheat the oven to 350°F (180°C). Line baking trays with parchment paper and set aside.
Add the butter to a stainless steel pan and brown it over medium heat. The butter will foam and crackle as it cooks. Stir occasionally to prevent burning. Once it smells nutty and is browned, remove from the heat.
Transfer the brown butter to a glass bowl and chill in the refrigerator.
Place the pumpkin purée on a stack of paper towels. Use fresh stacks of paper towels to absorb the excess liquid, continuing until the pumpkin has a soft, playdough-like consistency.
Once the brown butter has cooled, whisk in the brown sugar and granulated sugar for 1 minute, until the mixture resembles wet sand.
Whisk in the egg yolk, vanilla, and prepared pumpkin purée.
Add the flour, pumpkin spice, salt, and baking soda. Mix just until combined.
Refrigerate the dough for 10–15 minutes.
Scoop the dough using a heaping 2-tablespoon cookie scoop and roll each dough ball in the cinnamon sugar.
Place the dough balls on the prepared baking sheets, spacing them 2–3 inches apart.
Bake for 10–12 minutes.
Let the cookies cool on the baking sheet for 5–7 minutes.
Transfer the cookies to a cooling rack.
Enjoy warm or cooled.