Preheat the oven to 350 degrees. Coat the muffin tray in cooking spray.
Toast the walnuts in a large skillet over medium-low heat for about 5-7 minutes or until lightly browned and fragrant. Let cool and then chop coarsely.
In a large bowl, whisk together the flour, sugar, baking soda, baking powder, salt, ground cinnamon, and nutmeg. Stir in the nuts and half of the coconut. Set aside.
In a separate bowl, whisk together the eggs, oil, and vanilla extract.
Fold the wet ingredients, along with the grated carrot and apple, into the flour mixture, stirring just until moistened.
Pour evenly into the prepared muffin tray and top with the remaining coconut.
Bake for 20 - 25 minutes or until a toothpick inserted in the center comes out clean.
Remove from oven and let cool on a wire cooling rack.