Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper and set aside.
Whisk the dry ingredients in a medium bowl: flour, cornstarch, baking soda, cream of tartar, cinnamon, and salt.
In a large bowl, whisk together the oil, sugar, applesauce, and vanilla extract until smooth and well combined.
Add the dry mixture to the wet ingredients and mix until a thick dough forms. Use your hands if needed - the dough will be quite stiff.
Cover and chill the dough in the refrigerator for 30 minutes. This helps prevent spreading and gives the cookies a soft, chewy center. (Skip this step if you prefer thinner cookies with crackly tops.)
Make the cinnamon sugar coating by stirring together the sugar and cinnamon in a small bowl.
Scoop and roll the dough into golf ball-sized rounds (about 1½ tablespoons each), then roll each ball in the cinnamon sugar to coat.
Place cookies on the prepared baking sheets, spacing them 2 inches apart. For flatter cookies, gently press down each ball with the bottom of a glass.
Bake for 9–11 minutes, or until the edges look set and the bottoms are just lightly golden. Do not overbake - they will continue to firm up as they cool.
Tap the tray gently on the counter once after removing from the oven to help them settle. Let cookies cool on the tray for 10 minutes, then transfer to a wire rack to cool completely.