Preheat your oven to 350 degrees F. Line a muffin pan with paper, foil, or silicone liners, and set aside.
In a medium bowl whisk together the flour, baking soda, cinnamon and salt.
In a large bowl vigorously whisk together the butter, honey, egg and vanilla. Slowly add in the flour mixture until well combined. The batter will be fairly thick at this point.
Using a spatula, carefully fold in the applesauce and carrots. Divide the batter evenly among the muffin cups. Bake for 22 to 24 minutes or until a toothpick comes out clean and muffins are beginning to turn golden brown on top.
Recipe by Dallas Duo Bakes at http://dallasduobakes.com/2014/06/whole-wheat-carrot-applesauce-muffins.html