Preheat oven to 350 degrees F. Line a 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, use an electric mixer to mix the butter, honey, egg and vanilla together. Slowly add in the flour mixture until well combined. The batter will be fairly thick.
Using a spatula, carefully fold in the applesauce and carrots. Mix in walnuts, if desired. Divide the batter evenly among the muffin cups. Bake for 22 - 24 minutes or until a toothpick comes out clean.