Heat the oven to 375°F and line two baking sheets with parchment. Beat butter and dough sugar for 2 minutes, then beat in egg, yolk and vanilla.
Whisk flour, cream of tartar, baking soda and salt. Mix into the butter just until the flour disappears.
Combine coating sugar and cinnamon in a small bowl. Divide the dough into 24 balls and roll each in the cinnamon sugar.
Set 2 inches apart and bake one sheet at a time for 9 to 10 minutes, until the rims are set and the centers are puffed but soft.
Leave on the hot sheets for 5 minutes before transferring to racks; the centers will settle into wrinkles as they cool.