Brown the butter: in a medium light colored frying pan, melt the butter. Continue to cook the butter, stirring continuously to prevent burning. The butter will begin to froth, milk solids will form in the bottom, the color will shift from light yellow to a rich golden color, and it will give off a nutty aroma. Once the color changes to gold, transfer the butter to a bowl to stop cooking. Cool slightly for 10-15 minutes. You should yield 1/2 cup of browned butter.
Dry the pumpkin: While the butter cools, pat dry the pumpkin puree with paper towels to remove as much moisture as possible. You can also squeeze the pumpkin between layers of paper towel. This step is key to preventing cakey cookies, so don't skip this step. You should have about ¼ cup of dried puree.
Make the cookie dough: In a stand mixer fitted with the paddle attachment, cream together cooled browned butter, granulated sugar, and brown sugar. Fold in the vanilla extract, egg yolk, and dried pumpkin puree.
In a separate bowl, combine the flour, pumpkin pie spice, cream of tartar, baking soda, and salt and mix to distribute. With the mixer on medium speed add the flour mixture and mix until incorporated.
Chill the dough: Chill the dough for 30-60 minutes. Chilling will result in thicker, chewier cookies with less spread and gives the flavors more time to meld. You can skip this step if you prefer thinner, more spread out cookies. Take the cookie dough out when you start to preheat the oven.
Remove the cookie dough from the refrigerator. Preheat the oven to 350℉. Line a baking sheet with parchment paper or a silicone baking mat (optional, to reduce spreading).
In a small bowl combine the sugar and cinnamon for rolling the dough.
Roll and bake: Form the dough into roughly 2 tablespoon sized balls and roll all sides in the sugar-cinnamon topping (you should yield about 16 cookies). Space the sugared cookies a few inches apart on the prepared baking sheet. Bake for 10-12 minutes, or until the edges are set and the centers are puffed up and slightly underbaked in the middle. Cool the cookies completely on the baking sheet prior to serving.