Preheat oven to 400 °F (204 °C) and line a muffin tin with muffin cups.
In a large bowl, whisk together flour, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a medium bowl, stir together carrots, walnut, apple butter, maple syrup, vanilla extract, eggs, and coconut oil.
Pour wet ingredients into dry ingredients then stir gently until just mixed and incorporated.
Evenly divide batter amongst muffin cups, filling about 3/4 of the way to the top, then bake for 13-15 minutes, or until a toothpick inserted into the center of the muffin comes out clean.
Remove from oven then let cool completely on a wire cooling rack.
In the bowl of a stand mixer with the stand mixer fitted with the paddle attachment, beat together butter and cream cheese until light and fluffy. Add in powdered sugar, 1 cup at a time until frosting reaches desired consistency to frost or pipe. Don't forget to scrape down the sides with each addition of powdered sugar. Add in the vanilla extract and mix until incorporated. Garnish with more chopped walnuts on top.