Mix the dry ingredients.
In a medium bowl, whisk together the flour, cream of tartar, baking soda, and salt. Set aside.
Cream the shortening and sugar.
In a large mixing bowl, beat the shortening until smooth. Add the sugar and cream until light and fluffy, 2–3 minutes. Beat in the eggs one at a time until fully incorporated.
Combine the dough.
Add the dry ingredients to the wet mixture and mix just until no flour streaks remain. Do not overmix. Cover and chill the dough for at least 30 minutes.
Prepare the coating.
In a small bowl, stir together the sugar and cinnamon.
Shape the cookies.
Scoop dough into balls about the size of small walnuts (roughly 20–22 g each). Roll each ball in the cinnamon-sugar mixture to coat.
Bake.
Arrange the dough balls 2 inches apart on ungreased baking sheets.
Bake at 400°F (204°C) for 8–10 minutes, until the edges are lightly golden but centers are still soft. The cookies will puff up, then settle into crinkled tops as they cool.
Cool and serve.
Let cookies cool on the baking sheet for 2 minutes, then transfer to a rack to finish cooling.
Texture: Shortening produces puffier, softer cookies; butter yields more spread and richer flavor.
Make Ahead: Dough keeps 2 days in the fridge; freeze scooped dough balls up to 2 months.
Storage: Store baked cookies in an airtight container up to 5 days.
Doneness Cue: Cookies should look slightly underbaked in the center when removed — they finish setting as they cool.