Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large mixing bowl, cream together the softened butter, sugar, egg, and pumpkin puree until smooth.
In a separate bowl, mix the flour, cream of tartar, baking soda, salt, and pumpkin pie spice. Gradually add the dry ingredients to the wet mixture, mixing until a dough forms.
In a small bowl, mix together the sugar and cinnamon for the cinnamon sugar coating.
Roll the dough into 1-inch balls, then roll each ball in the cinnamon sugar mixture until coated evenly. Place the coated dough balls on the prepared baking sheet, spacing them evenly.
Lightly press down on each dough ball with the back of a spoon or your fingers to slightly flatten.
Bake in the preheated oven for 8-10 minutes, or until the edges are set and the cookies are just beginning to crack on top.
Remove from the oven and let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
