Whisk together the flour, cream of tartar, baking soda, and salt in a small bowl until well combined.
Using a hand mixer, beat together the butter, white sugar, and brown sugar in a large bowl, scraping down the sides, until well combined.
Slice the vanilla bean in half lengthwise, then scrape the seeds out with the back of your blade, add in the vanilla bean seeds to the mixture.
Add the egg and continue to beat until the batter is pale yellow and thickens, 3 minutes.
Gradually add the dry ingredients until just combined. Set the dough aside for at least 30 minutes to hydrate the flour.
Arrange a rack in the center of the oven; preheat to 400 degrees. Line a baking sheet with parchment paper.
Combine the white sugar and cinnamon together in a small ramekin.
Shape the dough into walnut-sized balls. Roll each ball in the cinnamon and sugar mixture until evenly coated. Place on the prepared baking sheet a few inches a part.
Bake for 7-9 minutes, until edges are lightly browned and firm but centers are puffed and soft.
Let cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely.