In a mixing bowl, whisk flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt and set aside.
In another mixing bowl, whisk oil, eggs, brown sugar, granulated sugar, applesauce, pineapple, and vanilla extract then add in shredded carrots and combine well.
Pour the wet ingredients into the dry ingredients and mix with a Dutch whisk or spatula/spoon until combined. Make sure you don’t overmix.
Pour batter into sheet pan sprayed with non-stick cooking spray and spread evenly.
Bake in a preheated 350 degree Fahrenheit oven for 25 minutes, or until a toothpick inserted comes out clean.
Remove and let cool completely before frosting.