Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt. Set aside.
In a large bowl, combine the granulated sugar, light brown sugar, and vegetable oil. Beat until well blended.
Add the eggs one at a time to the sugar and oil mixture, beating well after each addition.
Stir in the 2 teaspoons of vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the grated carrots, chopped walnuts, and drained crushed pineapple 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 before frosting.
To make the frosting, beat the softened cream cheese and unsalted butter together in a large bowl until smooth and creamy.
Gradually add the powdered sugar, one cup at a time, beating well after each addition.
Add 1 teaspoon of vanilla extract and beat until the frosting is light and fluffy.
Place one cake layer on a serving plate and spread a layer of cream cheese frosting over the top.
Place the second cake layer on top and frost the top and sides of the cake evenly.
Refrigerate the cake for at least 30 minutes before serving to allow the frosting to set.