Preheat oven to 350 degrees F (180 degrees C) and place rack in center of oven.
Toast the walnuts for about 8 minutes or until lightly browned and fragrant. Let them cool and then chop coarsely.
Peel and finely grate the carrots and apple. Set aside.
In a large bowl whisk together the flour, sugar, baking powder, salt, and ground cinnamon. Stir in the nuts and coconut. Set aside.
In a separate bowl whisk together the eggs, oil, and vanilla extract.
Fold the wet ingredients, along with the grated carrots and apple, into the flour mixture, stirring just until moistened. Evenly divide the batter between the prepared muffin cups and bake for 20 - 25 minutes or until a toothpick inserted in the center comes out clean.