Preheat oven to 350 degrees.

In a large mixing bowl, cream butter and sugar for 4-5 minutes until light and fluffy. Scrape the sides of the bowl and add the eggs and vanilla. Cream for 1-2 minutes longer.

Stir in flour, cream of tartar, baking soda, and salt, just until combined.

In a small bowl, stir together sugar and cinnamon.

If time allows, wrap the dough and let refrigerate for 20-30 minutes. Roll 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 the cookie balls are completely covered. To make flatter snickerdoodles, press down in the center of the ball before placing in the oven.

Place on a parchment paper-lined baking sheet. Bake for 9-11 minutes. Let cool for several minutes on baking sheet before removing from the pan.