Preheat the oven to 350 degrees F. Line a 12-cup muffin tin with paper liners or grease with butter, oil or cooking spray.
In a large bowl whisk the egg, applesauce, honey, butter, and vanilla. Stir in the flour, baking soda, cinnamon, and salt. Stir ingredients together until just combined and there are still some spots of flour remaining.
Fold in the shredded carrots and 1/2 cup of your favorite add-ins. Mix just until combined (don't overmix).
Bake for 15-20 minutes or until a toothpick inserted in the center of a muffin comes out clean. Cool for at least 10 minutes before serving. To store, cover with plastic wrap at room temperature for u to 3 days.