Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper or silicone mats.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt until evenly combined. Set aside.
In a large bowl, beat the softened butter and 3/4 cup sugar together with an electric mixer on medium speed until light and fluffy, about 2-3 minutes. The mixture should be pale and creamy.
Add the egg and vanilla extract to the butter mixture and beat until fully incorporated, scraping down the sides of the bowl as needed.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix — the dough should be soft and slightly sticky.
In a small shallow bowl, combine the 1/4 cup sugar and cinnamon, stirring until the cinnamon is evenly distributed throughout the sugar.
Scoop the dough into 1 1/2 tablespoon-sized balls (about 1.5 inches in diameter) and roll each ball generously in the cinnamon sugar mixture until completely coated.
Place the coated dough balls on the prepared baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, until the edges are set but the centers still look slightly soft and puffy.
Remove from the oven and let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack. They will flatten slightly as they cool and develop that signature crackled top.
