Preheat the oven to 350F degrees. Line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, cream of tartar, baking soda, salt, and spices. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, mix the butter and cream cheese together until smooth and creamy.
Add the pumpkin, 1 cup granulated sugar, powdered sugar, egg, egg yolk, and vanilla and mix until fully incorporated.
Slowly stir flour mixture into wet ingredients until dough comes together.
Roll dough into balls about the size of a golfball and place on the baking sheet. Repeat process with more dough until you have 10 or so balls spaced at least 2 inches apart.
Place the remaining 2 tablespoons of sugar into a small bowl. Coat the bottom of a glass with cooking spray, dip in the sugar, and flatten each dough ball to about 1/2-inch thickness. Spray more cooking spray on the bottom of the glass between batches, if needed.
Bake cookies for 7-9 minutes or until tops look mostly dry around the edges, yet still glossy right the center. You do not want any browning.
Remove from the oven and allow to cool on the baking sheet for 4-5 minutes before transferring to a wire rack to cool completely.
Beat the cream cheese and butter in a mixing bowl until smooth. Add the powdered sugar, ground cinnamon, and vanilla extract; beat until smooth and fluffy. Refrigerate leftovers.
Using a knife, swirl the frosting onto the cooled cookies until the tops are covered. Refrigerate in a single layer in an airtight container. Alternatively, store cookies at room temperature and only frost before serving.