Preheat oven to 350 degrees F. Line a muffin pan with paper or silicone muffin liners (or grease the pan).
In a large bowl, combine the whole wheat flour, baking soda, cinnamon, ginger, nutmeg, allspice, and salt. Whisk thoroughly.
In a small bowl, combine the melted butter, honey, egg, vanilla extract, and applesauce and whisk to combine. Pour the wet ingredients into the dry ingredients. Stir just until combined.
Fold in the shredded carrots, being careful not to over mix.
Scoop batter into your prepared muffin tin. Bake for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean. Let cool a few minutes before serving.