Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
Cream together butter, sugar, egg, and pumpkin puree in a large bowl until smooth.
Add flour, cream of tartar, baking soda, salt, and pumpkin pie spice. Mix until dough forms.
In a small bowl, mix sugar and cinnamon for the coating. Roll dough into 1-inch balls, then coat in cinnamon sugar.
Arrange dough balls on the baking sheet, spacing evenly, and slightly flatten each with the back of a spoon.
Bake for 8–10 minutes until edges are set and tops crack slightly. Cool for a few minutes on the baking sheet before transferring to a wire rack.