Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper. In the bowl of a stand mixer, cream together the softened butter and sugar on medium speed for 4 to 5 minutes until pale and fluffy. Scrape down the sides of the bowl, then incorporate the eggs and vanilla extract. Continue mixing for an additional 1 to 2 minutes until fully blended.
Add the flour, cream of tartar, baking soda, and salt. Mix on low speed just until the dry ingredients are combined, taking care not to overmix.
In a separate small bowl, combine the cinnamon and sugar for the coating. If time permits, chill the dough for 20 to 30 minutes to enhance flavor and texture.
Portion the dough into smooth, round balls using a cookie scoop. Roll each ball thoroughly in the cinnamon-sugar mixture, ensuring full coverage. For a second coating, spoon more of the mixture over the dough balls and gently roll again. To achieve a flatter cookie, lightly press down on the center of each ball before baking.
Arrange the coated dough balls on the prepared baking sheets, spacing them evenly. Bake for 9 to 11 minutes, or until the edges are set and the centers appear slightly underbaked. Let the cookies rest on the baking sheet for several minutes before transferring to a wire rack to cool completely.