Preheat your oven to 400°F (200°C).
To make the cookies, beat together the sugar, butter, shortening, eggs, and vanilla in a large bowl until smooth and creamy.
In another bowl, whisk together the flour, cream of tartar, baking soda, and salt.
Gradually incorporate the dry mixture into the wet ingredients, mixing just until combined.
Shape the dough into balls about the size of walnuts.
For the cinnamon-sugar coating, mix the sugar and cinnamon in a small bowl or a zip-top plastic bag.
Roll the dough balls in the cinnamon-sugar mixture until fully coated, then place them on ungreased baking sheets, spacing them 2 inches apart.
Bake in the preheated oven until the cookies are set but still soft, about 8 to 10 minutes, switching the baking sheets between racks halfway through.
Once baked, remove the cookies from the oven and transfer them immediately to wire racks to cool.