In a medium bowl, whisk together the flour, cream of tartar, baking soda, salt, and pumpkin pie spice until fully distributed, then set aside.
Spoon the pumpkin puree onto a few layers of paper towel, fold the towel over, and press gently for about 30 seconds to remove excess moisture; scrape the blotted puree into a small bowl.
In a large bowl, whisk the melted butter, brown sugar, and granulated sugar until no lumps remain, then add the blotted pumpkin puree, egg yolk, and vanilla and whisk until smooth, about 30 seconds.
Pour the dry ingredients into the wet ingredients and fold with a rubber spatula just until no streaks of flour remain, stopping as soon as the dough comes together.
Cover the bowl with plastic wrap and refrigerate for at least 1 hour, or up to 24 hours, to firm up the melted butter and prevent spreading.
Preheat the oven to 350°F (176°C), line two baking sheets with parchment paper, and stir together the granulated sugar and ground cinnamon in a small shallow bowl.
Using a medium cookie scoop, portion the chilled dough into balls of about 1.5 tablespoons, roll each briefly between your palms to smooth, then roll each ball in the cinnamon sugar until fully coated.
Place the coated dough balls about 2 inches (5 cm) apart on the prepared baking sheets and bake for 10 to 12 minutes, until the edges look set but the centers still appear slightly underbaked.
Let the cookies rest on the baking sheet for 5 minutes, then transfer to a wire cooling rack to cool completely; repeat with any remaining dough, reusing cooled parchment-lined sheets.