Mix together the flour, spices, cornflour, baking powder and salt.
With a hand mixer or stand mixer fitted with the whisk attachment, whisk together the oil, applesauce, vanilla and sugar until smooth and fluffy, for one minute.
Add the flour, a third at a time, and mix well after each addition with a spatula. Make sure you scrape down the sides and the bottom of the bowl.
Refrigerate the dough for about 30 minutes.
Using a small ice-cream scoop or with your fingers, scoop out about 1/4-inch balls of the dough and place them on a greased cookie sheet about an inch apart. Press down slightly with your fingertips or a spatula to flatten. If the dough is a little sticky, moisten your fingers and palms with some water to make it easier to handle.
Bake the cookies in a preheated 375-degree Fahrenheit oven for 12-14 minutes until the sides are lightly browned. Rotate the cookie sheet halfway through baking.
Remove the baked cookies to a rack and cool thoroughly.