Preheat your oven to 350°F and line two large baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt until well combined.
In a large bowl using a hand mixer or in the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter and 1 1/2 cups sugar on medium speed until light and fluffy, about 2-3 minutes.
Beat in the eggs one at a time, followed by the vanilla extract, scraping down the sides of the bowl as needed.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until the dough comes together and no dry streaks of flour remain.
In a small, shallow bowl, stir together the remaining 1/4 cup sugar and 2 tablespoons cinnamon.
Scoop the dough into 1 1/2 tablespoon-sized portions, roll into balls, and then roll each ball in the cinnamon-sugar mixture until thoroughly coated before placing them 2 inches apart on the prepared baking sheets.
Bake for 10-12 minutes, or until the edges are set and the tops are slightly cracked, then allow the cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.