Heat the oven to 375°F (190°C). Line 2 baking sheets with parchment paper.
Whisk the flour, cream of tartar, baking soda and salt in a bowl.
Beat the butter and 1 1/2 cups sugar for 2 to 3 minutes until fluffy. Beat in the eggs one at a time, then the vanilla.
Mix in the dry ingredients on low just until combined. If the dough is very soft, chill it for 30 minutes.
Mix the 1/4 cup sugar and cinnamon. Roll 1 1/2 tablespoon balls of dough in the cinnamon sugar and place 2 inches apart.
Bake one sheet at a time for 9 to 11 minutes, until the edges are set and the tops crackle.
Cool on the sheet for 5 minutes, then move to a wire rack.