Preheat the oven to 375°F (190°C). Line 2 baking sheets with parchment paper.
Measure 1.75 cups granulated sugar; in a small bowl combine 0.25 cup of the granulated sugar with ground cinnamon to make the coating.
In a medium bowl, whisk together all-purpose flour, cream of tartar, baking soda, and fine salt.
In a large bowl, beat unsalted butter with the remaining sugar on medium speed until pale and fluffy, 2–3 minutes.
Add eggs one at a time, beating well after each addition, then beat in vanilla extract.
Add the dry ingredients in two additions on low speed, mixing just until a soft dough forms; scrape the bowl to ensure no dry pockets remain.
Scoop 1.5-tablespoon portions of dough (about a #40 scoop), roll each into a ball, then roll in the cinnamon-sugar to coat. Arrange 12 per sheet, spacing about 2 inches.
Bake 9–11 minutes, rotating sheets halfway, until edges are set and tops are crackled while centers are just set and still puffy.
Cool on the sheets for 5 minutes, then transfer cookies to a rack to cool completely.