Cream together the butter, sugar, and ground cinnamon in the bowl of a stand mixer fitted with a paddle attachment on medium-high speed until light and creamy, about two minutes. Stop the mixer after one minute and scrape down the sides of the bowl. This step is important. A thick layer of butter clings to the side of the bowl. If you don’t scrape the bow and mix for an additional minute, that layer of butter can cause the cookies to spread.
Stop the mixer. Add the gluten-free flour, cream of tartar, baking soda, salt, and cinnamon. Blend until combined. Dough will be stiff.
Chill dough for 20 minutes. Prepare Cinnamon-Sugar Coating: stir together cinnamon and sugar in a small bowl.