Blot the pumpkin: spread the pumpkin puree on a plate lined with folded paper towels and press with more towels until very little moisture transfers. The puree will reduce by about a third — this step is not optional.
Whisk the dry ingredients: in a medium bowl, whisk together the flour, cream of tartar, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon.
Cream the butter and sugars: in a large bowl, beat the softened butter with the granulated sugar and brown sugar on medium speed for 2 to 3 minutes, until light and fluffy.
Add the wet ingredients: beat in the blotted pumpkin puree, egg, egg yolk, and vanilla until smooth and evenly orange.
Combine: add the dry ingredients in two additions, mixing on low just until no flour streaks remain. Do not overmix — overmixed dough bakes up tough.
Chill the dough: cover and refrigerate for 30 minutes (up to overnight). Chilled dough scoops cleanly and holds its thick shape in the oven.
Roll in spice sugar: stir together the coating sugars and spices in a small bowl. Scoop 1 1/2-tablespoon balls of dough, roll smooth, and roll generously in the spice sugar.
Bake: place 2 inches apart on parchment-lined baking sheets. Bake at 350°F for 11 to 13 minutes, until the edges are set, the tops are puffy and crackled, and the centers still look slightly soft.
Cool: let the cookies cool on the baking sheet for 5 minutes — they finish setting as they cool — then transfer to a wire rack to cool completely.