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 until well combined.
In a large bowl, beat the granulated sugar, brown sugar, and vegetable oil together until smooth.
Add the eggs one at a time to the sugar and oil mixture, beating well after each addition.
Stir in 2 teaspoons vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing just until 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 40 to 45 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 prepare the frosting, beat the softened cream cheese and unsalted butter together in a large bowl until creamy and smooth.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Stir in 1 teaspoon vanilla extract and continue to 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 evenly.
Refrigerate the cake for at least 30 minutes before serving to set the frosting.