Heat the oven to 375°F. Line three baking sheets with parchment paper.
Beat the butter and sugar on high speed until light and fluffy, 2 to 3 minutes.
Mix in the egg, drained pumpkin, and vanilla until smooth.
On low speed, add the flour, cream of tartar, baking soda, salt, and pumpkin pie spice. Mix just until no dry streaks remain.
Scoop rounded 1-tablespoon balls and set them on one of the lined sheets.