Place cupcake wrappers into muffin pan. Preheat oven to 350°F.
In a large bowl, combine flour, baking soda, baking powder, salt, cinnamon, ground ginger, and nutmeg; set aside.
In a separate bowl, whisk together the honey, vanilla, grapeseed oil, egg, egg whites, milk, and applesauce. Shred or grate carrots and stir into the mixture.
Add the wet ingredients to the dry, and stir until just combined. Fold in coconut, raisins, and walnuts.
Pour batter into muffin liners and bake for 25 minutes or until a toothpick inserted in the center comes out clean.
Cool on a wire rack for 5 minutes before serving.