Preheat oven to 350°. Grease a cookie sheet that is lined with parchment paper.
In the bowl of your mixer, cream together the butter and sugar.
Add the egg and vanilla and beat several minutes until light and fluffy.
In a smaller bowl, combine the flour, starch, salt, cream of tartar, baking soda, and xanthan gum. Add these dry ingredients to the mixing bowl. Combine on low speed until moistened then beat on medium speed about 30 seconds more.
In a very small bowl, combine the 2 Tablespoons sugar and the cinnamon.
Roll the dough into balls approximately 1 inch in diameter. Roll the balls in the cinnamon sugar.
Place them on the greased and lined cookie sheet about 2 to 3 inches apart. (Wipe and regrease the parchment paper between batches to help them spread evenly.)
Bake at 350° for 8 minutes.
Move cookies to a wire rack to cool.
Recipe by The Gluten-Free Homemaker at http://glutenfreehomemaker.com/gluten-free-snickerdoodles-perfect/