In a large bowl, combine the eggs, sugar and oil. Combine the flour, cinnamon, baking soda, baking powder, salt and nutmeg; beat into egg mixture. Stir in carrots.
Pour into 2 greased and floured 9-in. round baking pans. Bake at 350° for 35-40 minutes or until a toothpick inserted in center comes out clean. Cool for 10 minutes before removing from pans to wire racks to cool completely.
For frosting, in another large bowl, cream butter and cream cheese until light and fluffy, 3-4 minutes. Beat in vanilla. Gradually beat in powdered sugar. Add enough milk to achieve desired spreading consistency.
Once cake has fully cooled, spread frosting between layers and over top and side of cake. Sprinkle on walnuts.
Chill in fridge for a minimum of 30 minutes before serving.