Preheat the oven to 350 degrees.
Line the baking sheet with parchment and set aside.
In the bowl of a stand mixer, cream together the butter, brown sugar, and sugar.
Add in the egg and vanilla and mix until smooth.
Add in the flour, cornstarch, cream of tartar, baking soda, baking powder, cinnamon, and salt. Mix until the dough pulls away from the side of the bowl and the mixture is crumbly but presses together.
In a small bowl, combine the sugar and cinnamon for the coating. Set aside.
Divide the cookie dough into 9 equal-sized balls. Roll the dough in the cinnamon and sugar mixture to coat.
Place each cinnamon sugar-coated cookie dough ball on your baking sheet.
Using the bottom of a drinking glass or similar flat-bottom object, flatten the dough until it is about ¾ of an inch thick. Sprinkle with a little extra cinnamon and sugar mixture.
Bake in the preheated oven for 10 minutes. The cookies should be soft and chewy in the center so do not overbake.
Allow the cookies to cool while making the frosting.