In a large bowl whisk together the flour, baking powder, baking soda, and salt. Using the large tooth on a box grater, grate the apple and carrot.

In a stand mixer fitted with a paddle attachment, cream the butter and sugar until light and fluffy, scraping down the sides of the bowl with a rubber spatula as needed, about 5 minutes. Add the vanilla extract and eggs, one at a time, mixing well between each addition.

Add the flour mixture, grated apple, and carrot and remaining ingredients and mix until the dough is just combined. Cover the dough with plastic wrap and chill in the fridge for at least 30 minutes. Preheat the oven to 350° F. Spray a rimmed baking tray with nonstick cooking spray.

Using a medium ice-cream scooper, scoop the cookies onto the rimmed baking tray, spacing at least 1 inch apart. Bake for approximately 20 minutes or until the cookies are dry and golden brown.