Preheat the oven to 375°F. In a medium bowl mix whisk together the flour, cream of tartar, baking soda, and salt; set aside.
In a small bowl stir together the cinnamon and 4 tablespoons of sugar, set aside as well.
In a large mixing bowl, beat together the butter and 1½ cups of sugar using a hand mixer or in a stand mixer fitted with a paddle attachment. Beat until light and fluffy about 2-3 minutes.
Beat in eggs one at a time, then vanilla. Add in the dry ingredients a little at a time with the mixer on a low speed.
Roll dough into 2 tablespoon balls and roll in cinnamon and sugar mixture. Place on a greased cookie sheet or one lined with parchment paper. Right before baking place thumb into the center of the cookies and make an indent. (This makes the cookies come out nice and flat without domes.)
Bake at 375°F for 10-12 minutes or until golden on bottom. Remove from the baking sheet and let cool on a wire rack.
