Preheat oven to 350 degrees F. Spray muffin tins with nonstick cooking spray or line with paper liners. Set aside.
In a large bowl, whisk together the eggs, applesauce and maple syrup (or honey). Whisk in the melted butter.
Add the baking soda, salt, cinnamon, nutmeg, cloves, ginger and vanilla and whisk until well combined.
Use a rubber spatula to gently fold in the white whole wheat flour, oats and grated carrot. Be careful not to over-mix the batter. The batter will be thick.
Divide the batter evenly between 12 muffin cups, filling each cup almost to the top. Bake until a tester inserted into the center of a muffin comes out clean, about 18-20 minutes. (You can also make 36 mini muffins with this recipe. Mini muffins will take about 12-14 minutes to bake.)
Let cool in the pan for 5 minutes before removing muffins to a wire rack to cool completely.
Storage: The muffins freeze very well. If kept air-tight in a zip-top plastic bag, they will stay fresh in the freezer for 2-3 months. Defrost on the counter or in the microwave before enjoying. Muffins will keep at room temperature for 2-3 days.