Preheat oven to 350 degrees F. Line 18 muffin cups with paper liners
In a large bowl combine the dry ingredients. Stir in the shredded carrots and cranberries until evenly coated with flour mixture.
In a medium bowl, whisk together the eggs, oil, applesauce, and vanilla. Pour the egg mixture into the dry mixture and stir until fully incorporated.
Evenly divide the mixture between the prepared muffin cups
Bake for 15-20 minutes or until a toothpick comes out clean from the center. Allow to cool in the pan for 5 minutes before transferring to a wire rack