Preheat the 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, beat the softened butter and 1 ½ cups granulated sugar together until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract, mixing until well combined.
Gradually add the flour mixture to the wet ingredients, mixing until just combined.
In a small bowl, mix together the ¼ cup of granulated sugar and ground cinnamon for rolling.
Using a cookie scoop or tablespoon, form dough balls and roll them in the cinnamon sugar mixture until fully coated.
Place the rolled dough balls onto the prepared baking sheets, leaving about 2 inches of space between each cookie.
Bake in the preheated oven for 8-10 minutes, or until the edges are set but the centers are still soft.
Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.