Whisk the flour, cream of tartar, baking soda and salt in a medium bowl.
In a large bowl, beat the butter and sugar with a mixer on medium speed for 2 to 3 minutes, until pale and fluffy. Beat in the eggs one at a time, then the vanilla.
Add the dry ingredients and mix on low just until no dry flour remains.
Cover the bowl and chill the dough for 30 minutes.
Heat the oven to 375°F (190°C) and line two baking sheets with parchment. Stir the coating sugar and cinnamon together in a small bowl.
Scoop the dough into 1 1/2 tablespoon balls (about 35 g), roll them smooth, then roll each one generously in the cinnamon sugar. Place them 2 inches apart.
Bake one sheet at a time for 9 to 11 minutes, until the edges are set and the centers are puffed and still look slightly underdone.
Cool on the baking sheet for 5 minutes, then move to a wire rack.