Preheat the Oven and Prepare the Baking Sheets. Preheat your oven to 350°F and line two baking sheets with parchment paper or silicone baking mats.
Whisk Dry Ingredients. In a medium bowl, whisk together the flour, baking soda, cream of tartar, cinnamon, nutmeg, and salt. Set aside.
Cream the Butter and Sugars. In a large mixing bowl, beat the softened butter with the granulated sugar and brown sugar until light and fluffy, about 2-3 minutes.
Add Wet Ingredients. Add the pumpkin puree, egg, and vanilla extract to the butter-sugar mixture and mix until combined.
Combine Wet and Dry Ingredients. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix, as this can result in tougher cookies.
Roll in Cinnamon Sugar. In a small bowl, mix together the cinnamon and sugar for rolling. Scoop out about 1.5 tablespoons of cookie dough, roll it into a ball, and coat it in the cinnamon-sugar mixture.
Bake the Cookies. Place the coated cookie dough balls onto the prepared baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are set and the tops are slightly cracked.
Cool and Enjoy. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. Serve and enjoy!