Preheat oven to 375°F (190°C).
In a large bowl, cream together the butter and 1 ½ cups sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
In a separate bowl, whisk together the gluten-free flour, cream of tartar, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
In a small bowl, mix the 2 tablespoons of sugar and the cinnamon.
Roll the dough into 1-inch balls, then roll each ball in the cinnamon-sugar mixture.
Place the balls 2 inches apart on ungreased baking sheets.
Bake for 8 to 10 minutes, or until the edges are set but the centers are still soft.
Allow cookies to cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.