Preheat oven to 350 degrees F. Line muffin pan with paper, foil, or silicone liners, and set aside.
In a medium bowl, whisk together flour, baking soda, cinnamon, ginger, and salt.
In a large bowl fitted with an electric whisk (or beaters), mix the butter, honey, egg, and vanilla together on medium speed. Turn down the speed and slowly add in the flour mixture until well-combined. The batter will be fairly thick.
4. Using a spatula, carefully fold in applesauce and carrots. Divide 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.