Spread the pumpkin puree between layers of paper towels and press to blot out excess moisture. Set aside.
In a large bowl, beat the butter, granulated sugar and brown sugar on medium speed for 2 minutes until light and fluffy.
Beat in the blotted pumpkin, egg yolk and vanilla until combined.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, pumpkin pie spice, cinnamon and salt. Add to the wet ingredients and mix on low just until combined.
Stir the coating sugar, cinnamon and pumpkin pie spice together in a shallow bowl.
Scoop the dough into 1½-tablespoon balls, roll smooth, then roll in the cinnamon sugar.
Air fryer: Line the basket with parchment and preheat to 320°F for 3 minutes. Place 6 to 8 dough balls 2 inches apart, press each down slightly, and air fry for 7 to 8 minutes until the edges are set and tops are crackled. Rest 3 minutes in the basket before moving to a rack. Repeat with remaining dough.
Oven: Preheat to 350°F. Place dough balls 2 inches apart on parchment-lined sheets, press down slightly, and bake 10 to 12 minutes until edges are set. Cool 5 minutes on the pan, then transfer to a rack.