How to Make It
Preheat oven to 350°F. Line 2 baking sheets with parchment paper; set aside. In a bowl, stir together all-purpose flour, cream of tartar, baking soda, salt, and 2 teaspoons pumpkin spice. Set aside.
In a mixer, cream together butter, 1 cup sugar, and brown sugar until light and fluffy, about 4 minutes. Add eggs, one at a time, waiting for the first to fully incorporate before adding the next. Beat on medium-high for 4 minutes. Add pumpkin and mix on low until incorporated, then beat on medium until the pumpkin is no longer separated from butter-sugar mixture, about 3 minutes. Add dry ingredients and mix on low until just combined.
In a small bowl, mix together remaining 1/3 cup sugar and 1/2 tsp. pumpkin spice. Scoop out a 2 Tablespoon-sized portion of cookie dough and roll into a ball. Roll ball in spiced sugar mixture to coat. Transfer to prepared baking sheet. Repeat with remaining dough, leaving 2 inches between each cookie dough ball. Bake for 13 to 15 minutes, rotating halfway through, until edges are lightly browned and cookie tops are dry to the touch. Transfer to cool on wire rack.