Whisk together flour, pumpkin spice, baking soda, cream of tartar, and salt in a small bowl until combined. Set aside.
Cream together butter, 1/2 cup granulated sugar, and brown sugar in mixing bowl of electric mixer using paddle attachment for 1-2 minutes.
Mix in egg yolk and vanilla on low speed until combined.
Mix in pumpkin purée on low speed, making sure to scrape down sides.
Add dry ingredients and mix until combined.
Scoop into 8 balls (1/4 cup each) on a large plate lined with parchment paper and chill for 1 hour.
Preheat oven to 325°F. Line cookie sheets with parchment paper. Pour remaining 1/2 cup granulated sugar onto a small plate.
Roll chilled cookie balls into granulated sugar and place on cookie sheets, 2-3 inches apart, and bake 17-20 minutes until edges are browned and centers begin to set.
Remove from oven and cool completely.
Meanwhile, mix together all the ingredients for the cream cheese frosting with an electric mixture until smooth. Set aside.
Frost the cookies with the frosting, sprinkle with cinnamon suger, and enjoy!