Beat butter and shortening together until well-combined.
Mix in sugar until incorporated.
Add eggs and vanilla, and mix in until combined.
Stir in flour, cream of tartar, baking soda, and salt until just combined.
Cover, and chill dough for at least 1 hour.
Preheat oven to 375 F. Line baking sheets with parchment paper or silicone baking mats.
Stir together sugar and cinnamon in a small, shallow dish.
Using a 1 ½ tablespoon cookie scoop, scoop out balls of cookie dough.
Roll into balls, and then roll in cinnamon/sugar.
Place on cookie sheet, and barely flatten cookies.
Bake for 8-9 minutes. Cookies will be set but still look wet between the cracks.
Let cool on baking sheet.
Notes
Butter: I use salted butter. If using unsalted butter, increase the salt to 1/2 teaspoon.
Shortening: The shortening helps to make the cookies soft and helps them to keep their shape.
All-purpose flour: It's important to properly measure the flour. You can weigh the flour (click on "metric" for the weights) or sift/stir the flour to break it up. Lightly spoon the flour into the measuring cup and level. Avoid packing the flour.