Preheat the oven to 350°F (175°C). Line 2 baking sheets with parchment paper or silicone mats.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, salt, and pumpkin pie spice.
In a large bowl, beat the softened butter and 1 1/2 cups sugar until light and fluffy, about 2–3 minutes.
Beat in the eggs, pumpkin puree, and vanilla until smooth and well combined. Scrape down the bowl as needed.
Add the dry ingredients to the wet mixture and mix on low just until no dry flour remains. If using white chocolate chips, fold them in.
Cover and chill the dough for at least 30 minutes to prevent excessive spreading.
Meanwhile, combine the 1/3 cup sugar and cinnamon in a small bowl for the coating.
Scoop the chilled dough into 2-tablespoon portions and roll into balls. Roll each ball in the cinnamon-sugar coating to cover completely.
Place dough balls on the prepared baking sheets about 2 inches apart. Bake for 10–12 minutes, until the edges look set and the centers are still slightly soft.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.