In a large mixing bowl, cream butter and sugar for 4 to 5 minutes until light and fluffy. Scrape the sides of the bowl and add eggs and vanilla. Cream for 1 to 2 minutes longer.
Stir in flour, cream of tartar, baking soda and salt, just until combined. Wrap dough and refrigerate for 20 to 30 minutes.
In a small bowl, stir together sugar and cinnamon. Roll dough into small balls until round and smooth. Drop into the cinnamon-sugar mixture and coat well. Using a spoon, coat for a second time, ensuring balls are completely covered.
Place on a parchment-paper-lined baking sheet. Press down in the center of the balls to flatten cookies.
Bake for 9 to 11 minutes. Let cool for several minutes on a baking sheet before removing from the pan.