Preheat oven to 375°F and line baking sheets with parchment paper.
In a large bowl, cream together butter and 1 cup of sugar until light and fluffy. Beat in eggs one at a time, then add vanilla extract.
In a separate bowl, whisk together flour, cream of tartar, baking soda, and salt. Gradually mix dry ingredients into the butter mixture until well combined.
In a small bowl, combine the remaining ½ cup sugar with cinnamon and stir well.
Roll dough into 1½-inch balls, then roll each ball generously in the cinnamon-sugar mixture to coat completely.
Place cookies 2 inches apart on prepared baking sheets.
Bake for 8-10 minutes until edges are set but centers are still soft. Cookies will puff up during baking and flatten as they cool.
Cool on baking sheet for 5 minutes before transferring to a wire rack. Store in an airtight container for up to 5 days.