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 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 until evenly distributed.
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.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes.
Turn the cakes out onto wire racks and cool completely.
To make the frosting, beat the softened cream cheese and butter together until smooth and creamy.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Add 2 teaspoons vanilla extract and beat until the frosting is light and fluffy.
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 allow the frosting to set.