Preheat oven to 375°F. Line two baking sheets with parchment.
Whisk flour, cream of tartar, baking soda, and salt in a medium bowl.
Beat butter and 1.1 cups sugar until pale and fluffy, about 2 minutes.
Mix in eggs and vanilla until smooth and combined.
Stir dry ingredients into the butter mixture just until a soft dough forms.
Combine 1/4 cup sugar and cinnamon in a small bowl for coating.
Scoop 1.5-tablespoon portions, roll into balls, then coat in cinnamon sugar.
Arrange on sheets 2 inches apart. Bake 8–10 minutes, edges set, centers soft.
Cool on the sheet 2 minutes, then move to a rack to finish cooling.