Preheat oven to 350°F. Line a muffin tin with paper cups or spray with cooking spray. Set aside.
In a large mixing bowl, combine the flour, baking soda, cinnamon, nutmeg, salt, carrots, raisins, and walnuts until well mixed. Set aside.
In a small mixing bowl, combine the apple butter, honey or maple syrup, eggs, vanilla, and butter. Stir until smooth.
Add the apple butter mixture to the flour mixture and stir to combine. Do not over mix (this results in tough muffins), a few lumps of flour are fine.
Spoon the mixture into the prepared muffin cups, filling them ⅔ of the way. Bake in preheated oven for 15-20 minutes, or until the tops begin to crack and a toothpick inserted into the center comes out clean.
Remove from the oven and let cool completely on a baking rack.
Make the frosting by combining the cream cheese and honey or maple syrup until smooth. Spread onto cooled muffins.