Brown the butter first. Melt the butter in a light-colored skillet over medium heat, stirring often. After about 5 to 7 minutes, the butter will foam, then the foam will settle and you will see golden-brown bits forming at the bottom. It should smell nutty and toasty. Pour it immediately into a large mixing bowl and let it cool to room temperature, about 20 minutes. You can speed this up by setting the bowl in the refrigerator.

Blot the pumpkin puree with a few layers of paper towels to remove some of the excess moisture. Press and blot a couple of times until the towels are barely damp. This step keeps the cookies from being too soft to roll.

Once the brown butter is cool and slightly solidified, add the granulated sugar and brown sugar. Beat with a hand mixer on medium for about 2 minutes until combined. Mix in the blotted pumpkin puree, egg yolk, and vanilla until smooth.

In a separate bowl, whisk together the flour, cream of tartar, baking soda, salt, cinnamon, ginger, nutmeg, and allspice. Add the flour mixture to the butter mixture and stir until a soft dough forms. It will be stickier than a classic snickerdoodle dough.

Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes. Do not skip this step. Chilling firms the dough enough to roll into balls and keeps the cookies from spreading flat.

Preheat your oven to 375 degrees F. Line baking sheets with parchment paper. Mix the rolling sugar and cinnamon in a small shallow bowl.

Scoop the chilled dough using a medium cookie scoop, about 1 1/2 tablespoons per ball. Roll each ball in the cinnamon sugar until fully coated, then place on the lined baking sheet about 2 inches apart.

Bake for 10 to 12 minutes. The edges should look set and the centers will still look slightly underdone and puffy. That is exactly right. Do not wait for them to look fully done in the oven, they will firm up on the hot pan.

Let the cookies cool on the pan for 8 to 10 minutes before transferring to a wire rack. Moving them too early will cause them to fall apart since the centers are still soft.

Once fully cooled, store in an airtight container at room temperature. They develop a slightly chewier texture by day two.