Preheat the oven to 350ºF and spray a muffin tin with nonstick cooking spray.
In a large mixing bowl add flour, sugars, baking soda, baking powder, salt, cinnamon, and nutmeg and stir. Set aside.
In a medium bowl add oil, eggs, applesauce, milk, and vanilla. Use a hand mixer to mix to combine.
Slowly add the wet mixture to the dry mixture and stir until combined using a spatula until combined.
Lastly stir in the shredded carrots.
Fill each muffin well ¾ of the way full (I used a ¼ cup scoop to make sure they are the same size). Bake the cupcakes at 350ºF until a toothpick inserted comes out clean- about 20-25 minutes.
Allow the cupcakes to cool completely before icing them.
Enjoy!