Preheat oven to 375°F (190°C) and line two baking sheets with parchment paper.
Whisk together flour, cream of tartar, baking soda, and salt in a medium bowl.
Beat softened butter and 1 ½ cups granulated sugar with a mixer on medium speed for 3–4 minutes until light and fluffy.
Add eggs one at a time, scraping down the bowl between additions, then mix in vanilla extract.
Gradually add the dry ingredients to the wet mixture on low speed until just combined.
In a small shallow bowl, mix 3 tablespoons sugar and 1 tablespoon ground cinnamon for the coating.
Scoop 1 ½ tablespoons of dough, roll into balls, and coat generously in the cinnamon sugar mixture.
Place coated dough balls 2 inches apart on prepared baking sheets.
Bake for 8–10 minutes until edges are set but centers appear slightly underdone.
Cool on baking sheets for 5 minutes, then transfer to a wire rack to cool completely.
