Preheat oven to 325. Lightly grease three 9-in diameter cake pans with 1 1/2 inch high sides. Line bottom of pans with waxed paper. Lightly grease waxed paper.
Using electric mixer, beat sugar and vegetable oil in bowl until combined. Add eggs 1 at a time, beating well after each addition. Sift flour, baking powder, baking soda, salt, cinnamon and nutmeg into sugar and oil mixture. Stir in carrots.
Pour batter into prepared pans, dividing equally. Bake until toothpick inserted into center comes out clean and cakes begin to pull away from sides of pans, about 45 minutes. Cool in pans on racks 15 minutes. Turn out cakes onto racks and cool completely.
Using electric mixer, beat powdered sugar, cream cheese, butter and vanilla in medium bowl until smooth and creamy. Place 1 cake layer on platter. Spread with 3/4 c frosting. Top with another cake layer. Spread with 3/4 c frosting. Top with remaining cake layer. Using icing spatula spread remaining frosting in decorative swirls over sides and top of cake. Serve cake cold or at room temperature.