Melt the butter in a light-colored pan over medium heat until it smells nutty and turns golden, about 4 to 5 minutes. Scrape it into a bowl and let it cool for 10 minutes.
Blot the Pumpkin
Spread the pumpkin on paper towels and press more on top to pull out the moisture, until it is noticeably drier.
Mix the Dough
Whisk the cooled butter with both sugars, then stir in the egg yolk, vanilla, and blotted pumpkin. Add the flour, pumpkin pie spice, baking soda, cream of tartar, and salt and stir until just combined.
Roll and Bake
Stir the coating sugar and cinnamon together in a small bowl. Scoop 16 dough balls, roll each in the cinnamon sugar, and space them on lined pans.
Bake at 350F for 10 to 12 minutes, until the tops are crackled but the centers still look soft. Cool on the pan for 5 minutes.
Notes
Blot the pumpkin: The drier it is, the chewier the cookie.
Yolk only: The white puffs pumpkin cookies into cake.
Keep the cream of tartar: It gives snickerdoodles their signature tang.
Don't overbake: Pull them while the centers still look soft.