Preheat the oven to 350 degrees F. Line two cookie sheets with parchment paper or silicone baking mats. With a stand mixer or electric hand mixer, cream together the softened butter with one cup sugar until pale and fluffy. Add the pumpkin, two egg yolks and vanilla extract. Beat again until smooth and well combined.
In a separate bowl, whisk together the flour, pumpkin spice, cream of tartar, baking soda and salt. Add the flour mixture to the bowl with the pumpkin mixture. Start on low speed and gradually increase the speed until a cohesive dough is formed. Scrap down the bowl as necessary with a rubber spatula while mixing. Refrigerate the dough for one hour. This helps to make sure the flour fully hydrates and that the cookies don't spread too much while baking.
In a shallow small bowl, stir together the 1/4 cup sugar with the pumpkin pie spice until well combined. Use a medium cookie scoop (1.5 tablespoon capacity) to form the cookie dough into 21 balls. Roll each ball in the pumpkin spice sugar mixture. Divide the cookies evenly between the two prepared cookie sheets.
Bake at 350 for 12 -13 minutes, rotating the baking pans front to back and top to bottom halfway through baking time. Allow the cookies to cool on the cookie sheets for 10 minutes before removing them to a wire rack to finish cooling.