Preheat oven to 350°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt.
In the bowl of a stand mixer, beat the butter until smooth, about 2 minutes. Scrape down the sides of the bowl.
Add the granulated sugar and brown sugar. Beat for 2 minutes, until light and fluffy. Scrape down the sides of the bowl.
Add the egg and vanilla. Beat until smooth and combined. Scrape down the sides of the bowl.
Add the flour mixture. Briefly beat the dough together until most of the flour is incorporated. Scrape down the sides of the bowl.
Beat for a few more seconds until the flour is fully incorporated.
Use a cookie scoop (or spoon) to create evenly portioned cookies. Use your hands to roll each portion into a smooth ball.
In a small bowl, stir together the granulated sugar and cinnamon for the topping.
Roll each dough ball in the cinnamon sugar topping and arrange them on the parchment-lined baking sheets, about 2 inches apart.
Bake for 8-12 minutes, until the edges are barely set. The centers will be pale and puffy, but will continue to bake on the tray as they cool.
Transfer the baking sheet to a cooling rack and working quickly, use two butter knives or spoons to press in the edges to compact the cookie and achieve a uniformly soft and chewy snickerdoodle.
Let the cookies cool on the pan for 3-5 minutes before transferring to a cooling rack.
While the cookies are still warm, dip the top of each cookie in the cinnamon sugar topping (you can use the leftover from step 9 or make a fresh batch).
Notes
Store in an airtight container at room temperature for up to 5 days, or in the freezer for up to 6 months.