Preheat the oven to 350°F (180°C) and grease a 13x9-inch baking dish. Set aside.
In a large bowl combine sugar, vegetable oil, and eggs with a spatula. Add grated carrots and orange zest. Mix until combined.
In a small bowl combine flour, baking powder, baking soda, cinnamon, and nutmeg. Sift the dry mixture into the bowl with the wet ingredients.
Mix together until just combined.
Pour mixture into prepared baking dish and bake for 20 minutes or until a toothpick inserted in the center comes out clean.
Allow cake to cool down completely before frosting it.
To make the frosting, beat together butter and confectioners' sugar in the bowl of a stand mixer fitted with the paddle attachment until light and fluffy.
Add vanilla extract and cream cheese and beat until blended. Frost cooled cake.