1. Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
2. In a medium bowl, whisk together the flour, cream of tartar, baking soda, salt, cinnamon, and nutmeg. Set aside.
3. In a large bowl, cream the softened butter and 1 1/2 cups of sugar together using a hand mixer until light and fluffy, about 3-4 minutes.
4. Add the pumpkin puree, egg, and vanilla extract to the butter mixture, beating until well combined.
5. Gradually mix the dry ingredients into the wet ingredients, ensuring no dry flour remains.
6. In a small bowl, combine the remaining 1/4 cup of sugar and pumpkin pie spice for rolling the cookies.
7. Using a cookie scoop or tablespoon, portion out the dough and roll each ball in the sugar mixture, ensuring an even coating.
8. Place the dough balls onto the prepared baking sheets, spaced about 2 inches apart.
9. Bake for 10-12 minutes, or until the edges are set and the tops are slightly cracked.
10. Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.

Remember to keep an eye on them during the final minutes of baking to avoid over-baking, which can cause the cookies to lose their soft centers.