Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt. Set aside.
In a large mixing bowl, cream together the softened butter and 1 ½ cups granulated sugar until light and fluffy, about 2-3 minutes.
Beat in the egg and vanilla extract until well combined.
Gradually mix in the dry ingredients until just blended - do not overmix.
In a small bowl, combine ¼ cup granulated sugar with the ground cinnamon.
Scoop out tablespoon-sized portions of dough and roll them into balls. Roll each ball in the cinnamon-sugar mixture until fully coated.
Place the coated dough balls onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers may look slightly underbaked; they will firm up as they cool.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.