Preheat oven to 350 degrees F.
In a large bowl, mix the flour, baking powder, baking soda and salt together with a fork.
In another bowl, mix the olive oil, sugar, egg, apple sauce and vanilla with a hand held mixer.
Pour half of the dry ingredients into the bowl of the wet ingredients and mix with your hand-held mixer. Add the other half of the dry ingredients and mix again. You may need to scrape the sides of the bowl as you do this.
Using a small cookie scoop, or a spoon, scoop out 1 Tbs sized balls of the dough and place on a cookie sheet.
Note: if you want to roll the dough in coarse sugar, do this prior to placing the balls of dough on a cookie sheet.
Bake for 10-12 minutes, then remove the cookies from the oven and let them sit on the cookie sheet for 5 minutes before moving them to cool on a cookie rack.