Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together the gluten-free all-purpose flour, baking soda, cream of tartar, and salt.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until smooth. Add the egg and vanilla extract, mixing until fully blended.
Gradually add the dry ingredients to the wet mixture, stirring gently until a dough forms.
In a small bowl, combine the 2 tablespoons of granulated sugar and 1 teaspoon of ground cinnamon. Roll about 1 tablespoon of dough into a ball and coat it in the cinnamon-sugar mixture.
Place the coated dough balls on the prepared baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes until the edges are lightly golden and the centers remain soft.
Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.