Pre-heat your oven to 350°F. Lightly grease and flour the inside of a 9"x13" baking pan (or two 9" rounds).
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, salt, white sugar and brown sugar.
Stir in the vegetable oil and melted butter until well combined.
Add the eggs one at a time, mixing well after each addition.
Stir in the vanilla extract.
Stir in the grated carrot and nuts. Mix until well combined.
Pour the batter into your prepared pan(s) and bake for about 40 minutes or until a tester comes out clean when inserted into the centre of the cake.
Allow the cake to cool for 10 minutes before inverting onto a cooling rack. Allow to cool completely before frosting.