Measure 1/3 cup of pumpkin puree onto a plate lined with several paper towels.
Place additional paper towels over the pumpkin and gently press to absorb the excess moisture. Repeat with fresh paper towels as needed until the pumpkin feels noticeably drier and is closer to a soft paste than a wet puree.
Don't skip this step! Removing some of the water helps give these cookies their chewy texture instead of making them cakey.
In a large mixing bowl, whisk together the melted butter, brown sugar and granulated sugar until smooth.
Add the blotted pumpkin, egg yolk and vanilla and whisk again until everything is well combined.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, salt, cinnamon and pumpkin pie spice.
Add the dry ingredients to the wet ingredients and gently mix until a soft cookie dough forms. Don't overmix.
Cover the dough and refrigerate for about 30 minutes. You want it firm enough to scoop and roll but not completely hard.
While the dough chills, combine the granulated sugar and cinnamon in a small bowl.
Preheat the oven to 350°F and line baking sheets with parchment paper.
Scoop the chilled cookie dough into large balls, using approximately 3 tablespoons of dough per cookie.
Roll each ball generously in the cinnamon sugar until completely coated.
Place the cookies several inches apart on the prepared baking sheets. These cookies are supposed to spread, so give them plenty of room.
Bake at 350°F for 11–14 minutes, or until the edges are set but the centers still look slightly underdone.
Don't wait for the centers to look completely baked before pulling them from the oven. They'll continue cooking on the hot baking sheet as they cool, which helps keep the centers chewy.
For especially round cookies, carefully swirl a large round cookie cutter around each cookie immediately after it comes out of the oven.
Let the cookies cool on the baking sheet for about 10 minutes before transferring them to a cooling rack.