Heat the oven to 350 degrees. Grease and flour 3 (8-inch) round cake pans.
In large bowl, beat the sugar, oil and eggs until creamy. Add ¾ cup sour cream and 2 teaspoons vanilla; beat until well-mixed. Add flour, baking soda, cinnamon, salt, and nutmeg. Beat on low speed until mixed. Beat on medium speed for 1 minute. Stir in the carrots and nuts. Pour the batter evenly into the pans.
Bake for 20 to 30 minutes or until toothpick inserted in center comes out clean. Cool in the pans for 10 minutes. Remove the cakes from pans onto cooling racks; cool completely, about 1 hour.
In a medium bowl, combine powdered sugar, 1/3 cup softened butter, 1/2 cup sour cream, and 1 teaspoon vanilla; beat on low speed until mixed. Beat on medium speed until smooth and creamy.
Place 1 cake layer, rounded side down, on a serving plate. Tuck strips of waxed paper under bottom edge of cake all around cake. Spread about 1/2 cup frosting over cake.
Place second layer over frosting, rounded side up. Repeat with third layer. Frost the sides and top of the cake. Remove the strips of waxed paper. Store covered in refrigerator.