Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, whisk together flour, baking powder, cinnamon, nutmeg, and salt.
In another bowl, combine vegetable oil, granulated sugar, and brown sugar. Add eggs one at a time, beating well after each addition.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in grated carrots and chopped walnuts.
Pour batter into prepared pan. Bake for 40 minutes or until a toothpick inserted into the center comes out clean. Let cool completely.
For the frosting, beat together cream cheese and butter until smooth. Gradually add powdered sugar and vanilla extract, beating until creamy.
Spread frosting over cooled cake. Slice and serve.