Line two baking sheets with parchment paper and set aside. In a large mixing bowl, beat together the butter and sugar until combined. This is easiest done in a stand mixer since we're working with butter straight from the fridge. Add in the vanilla extract and egg and beat until just combined. Then add in the flour, salt, and cream of tartar, and beat until a firm dough forms.

Form the dough into a ball on a piece of parchment paper, and cover it with another sheet of parchment. Optionally, you can just do this directly on a clean counter dusted with flour. Roll the dough out to about 1/4-1/2 inch thick- you want it to be fairly thick, slightly thicker than you might do for a cutout sugar cookie. Remove the top layer of parchment paper if using.

In a small bowl, stir together the sugar and cinnamon until well combined. Evenly sprinkle the mixture all over the rolled out dough. It's going to seem like a lot of cinnamon/sugar, but this is ok! Use your rolling pin to gently press the mixture into the dough. Then, use a knife to slice the dough into mini diamond shapes. I like to slice it into thin strips, about 1/2 - 3/4 inch wide, and then repeat the process in the other direction at a slight angle to get the diamond shape.

You're going to end up with a lot of cookies here- they should be very small! Gently lay out the cookies on your prepared baking sheets- they do not need much space between them because they won't spread at all during baking. Place the cookie sheets in the fridge while you preheat your oven to 350 degrees. Once the cookies have chilled for 20 minutes, place one sheet of cookies into the oven and bake for 6-8 minutes, or until the sugar topping has darkened slightly and the cookies are barely browning on the edges. Repeat for the second tray of cookies, and cool before serving!