Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, combine the granulated sugar, brown sugar, and vegetable oil. Beat in the eggs one at a time, then stir in 2 teaspoons vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the grated carrots, chopped walnuts, and drained crushed pineapple until evenly distributed.
Pour the batter into the prepared 9×13 inch pan and spread evenly.
Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
To make the frosting, beat the softened cream cheese and butter together in a medium bowl until smooth and creamy.
Add the powdered sugar gradually, beating until smooth and fluffy.
Mix in 1 teaspoon vanilla extract.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top.
Slice into 12 pieces and serve.