Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a mixing bowl, cream together the butter and 1.5 cups of sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition.
In a separate bowl, whisk together the flour, cream of tartar, baking soda, and salt. Gradually add to the butter mixture, mixing until just combined.
In a small bowl, mix together the 2 tablespoons of sugar and ground cinnamon.
Shape the dough into 1-inch balls and roll in the cinnamon-sugar mixture. Place 2 inches apart on the prepared baking sheet.
Bake for 8-10 minutes, or until the edges are set and the centers are soft. Cool on the baking sheet for 2 minutes before transferring to wire racks to cool completely.