In a medium bowl, whisk together the flour, baking soda, cream of tartar, pumpkin pie spice, and salt (omit salt if using salted butter).
In a stand mixer fitted with the paddle attachment, beat the softened butter, granulated sugar, and brown sugar on medium-high speed for 2–3 minutes, until light and fluffy.
Scrape down the bowl. Add the egg yolk, pumpkin puree, maple extract, and potato flake starter. Mix until combined, then beat again on high until fluffy.
Switch to the paddle attachment. On low speed slowly add the dry ingredients. Mix just until incorporated. Scrape the bowl well to ensure everything is mixed, especially on the bottom.
Cover the bowl with plastic wrap and refrigerate to ferment 24 hours up to 4 days.For a quicker ferment: leave on the counter 12 hours, then refrigerate at least 2 hours. For no fermentation: chill 2 hours and bake.
When ready to bake, preheat oven to 350°F. Line baking sheets with parchment paper.
Stir together the coating sugar, cinnamon, and pumpkin pie spice.
Scoop dough using a 1 Tbsp cookie scoop, roll each portion in the cinnamon-sugar mixture, and place on prepared baking sheets about 2 inches apart. Lightly flatten each dough ball.
Bake on the middle rack for 8 minutes.
Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.