Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper or lightly grease.
Beat 1 1/2 cups white sugar, butter, and eggs together in a bowl using an electric mixer until smooth and creamy. Combine flour, cream of tartar, baking soda, and salt in a separate bowl; stir into creamed butter mixture until dough holds together.
Mix 2 tablespoons white sugar and cinnamon together in a bowl.
Form dough into 2-teaspoon-size balls and roll in the cinnamon-sugar mixture. Place dough balls, about 2 inches apart, on the prepared baking sheet.
Bake in the preheated oven on the center rack for 7 minutes. Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.
