Cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined. Add the pumpkin puree and molasses, mixing until evenly incorporated.
In a separate bowl, whisk together the all-purpose flour, pumpkin pie spice, cream of tartar, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Wrap the dough tightly in plastic wrap and refrigerate for at least 30 minutes.
Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a small bowl, combine granulated sugar and cinnamon for the coating. Roll the chilled dough into 1-inch balls and then roll each ball in the cinnamon-sugar mixture.
Place the coated cookie dough balls onto the prepared baking sheet, leaving about 2 inches between each cookie. Bake for 10-12 minutes.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.