Line two baking sheets with silicone baking mats or parchment paper. Set aside.

Place the butter, granulated sugar, and brown sugar in a medium bowl. Use a mixer to beat on medium speed until well combined, about 1 minute. Add the pumpkin purée and vanilla extract and continue to beat until smooth, about 30 seconds.

Add the flour, cornstarch, pumpkin pie spice, cream of tartar, baking soda, baking powder, and salt to the bowl. Beat on low speed, scraping the sides of the bowl with a rubber spatula as needed, until a smooth dough forms.

Preheat the oven to 350°F.

Divide the cookie dough into 16 balls, using roughly 1 1/2 tablespoons of dough for each, and arrange them spaced 1 1/2 inches apart on the baking sheets. Transfer the sheets to the freezer for 10-15 minutes. Alternately, freeze the dough balls on a small tray or large plate and transfer to the baking sheets after freezing.

Bake the cookies on middle rack of oven until puffy and golden brown at the edges, 14-17 minutes.

Check to see that cookies are done. Remove from oven or add time as needed.

Allow the cookies to rest on the sheets for 5-10 minutes, then transfer to a wire rack to cool completely before serving