Cream together butter and shortening until well incorporated together. Add sugar and beat on high speed for at least 2 minutes.
Add eggs and vanilla, and beat an additional 1-2 minutes.
Stir together flour, cream of tartar, baking soda, and salt. Add to butter mixture and mix together on low until flour is incorporated. Do not overbeat at this step. Refrigerate dough for 24 hours, if possible, or at least 30 minutes.
When ready to cook, preheat oven to 400 degrees. Shape dough into rounded spoonfuls (I use a 2 tbsp. stainless scoop). Roll cookie dough balls into cinnamon sugar mixture, making sure dough is completely covered.
Bake for 8-10 minutes. Cookies should just begin to have a small amount of brown on the edges, but will still look mostly light. You don't want to overcook or you will end up with crispy cookies. Cool on cookie sheet for a couple of minutes before transferring to a cooling rack.