Preheat the 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, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, beat together the granulated sugar, brown sugar, and vegetable oil until well combined.
Add the eggs one at a time, beating well after each addition. Stir in 2 teaspoons vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots, chopped walnuts, crushed pineapple, and shredded coconut.
Divide the batter evenly between the prepared cake pans and smooth the tops.
Bake for 35 to 40 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 in a large bowl until smooth and creamy.
Gradually add the powdered sugar, beating until light and fluffy.
Stir in 1 teaspoon vanilla extract.
Once the cakes are completely cool, spread a layer of frosting on top of one cake layer.
Place the second cake layer on top and frost the top and sides of the entire cake.
Refrigerate the cake for at least 30 minutes before serving to set the frosting.