Preheat oven to 375°F. In a medium bowl, whisk together the flour, cream of tartar, and baking soda.
In the bowl of a stand mixer, beat the butter and 1 1/3 cups of sugar on medium speed until fluffy. Beat in the eggs and vanilla until smooth, scraping down the sides with a spatula as necessary. Reduce the mixer speed to low and beat in the dry ingredients mix (~1/3 of the bowl at a time) until well combined.
In a small bowl, whisk together the remaining 1/4 cup sugar and ground cinnamon. Scoop out the dough and with your hands shape them into small 1-inch balls. Gently toss them in the bowl with the cinnamon sugar until entirely coated. Place the balls on a large ungreased cookie sheet, with ~1 inch separation. Bake the cookies for ~12 minutes, or until lightly golden and crinkly on top. When done, cool the cookies on a wire rack and repeat with remaining dough.