Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the pumpkin puree, egg, and vanilla extract until well combined.
In a separate bowl, whisk together flour, baking soda, cinnamon, pumpkin spice, cream of tartar, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
In a small bowl, combine brown sugar and cinnamon-sugar coating for rolling.
Scoop tablespoon-sized dough balls and roll each in the cinnamon-sugar mixture.
Place the coated dough balls onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10 minutes or until the edges are set but the centers remain soft.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.