Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a large bowl, combine the granulated sugar, brown sugar, and vegetable oil. Beat in the eggs one at a time, then stir in the vanilla.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots, grated apples, walnuts, and coconut.
Divide the batter evenly between the prepared cake pans.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans for 10 minutes, then turn out onto wire racks to cool completely.
To make the frosting, beat the cream cheese and butter together until smooth. Gradually add the powdered sugar, beating until fluffy. Stir in the vanilla extract. If the frosting is too thick, add milk a tablespoon at a time until the desired consistency is reached.
Frost the cooled cakes, layering one on top of the other. Top with chopped fresh apples
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