Preheat oven to 375 degrees F. and line two baking sheets with parchment paper.
In a medium bowl, use a whisk to combine the flour, pumpkin pie spice, cream of tartar, baking soda, and salt.
Using an electric hand mixer or stand mixer fitted with the paddle attachment at medium speed, beat together the shortening, butter, granulated sugar, and brown sugar until it is light colored and fluffy, approximately 2 minutes.
Add the canned pumpkin and continue mixing until incorporated.
Turn the mixer down to low and slowly add the flour mixture until just combined, approximately 30 seconds. Use a rubber spatula to scrape down the sides and give the cookie dough a final mix by hand to ensure the flour mixture is incorporated.
For the coating, combine ¼ cup granulated sugar and the cinnamon in a shallow dish.
Scoop dough into 2 Tablespoon-sized portions and gently roll into balls with your hands.
Roll each ball in the prepared cinnamon sugar, coating generously.
Place balls on 2 parchment-lined baking sheets approximately 2 inches apart.
Place in oven and bake cookies one sheet pan at a time, rotating pan halfway through, for 10 to 12 minutes total.
Remove from oven when the cookie edges are starting to set and are lightly browned. The centers will remain soft and puffy.
Cool on the baking sheet for 10 minutes, the cookies will flatten and crackle on top as they cool, then transfer to a wire rack to finish cooling completely.