Preheat oven to 350º F. Grease cake pans and flour lightly.
In a large bowl, beat eggs until foamy, add sugar, then add the oil in a thin stream while beating.
Beat very well to make sure the mixture emulsifies.
Mix the flour, cinnamon, and baking soda and add to the egg mixture. Mix well.
Fold in the carrots and nuts, turn out into the prepared pans.
Bake for 35 - 40 minutes, or until toothpick comes out clean.
Cool about 10 minutes in the pan, then turn out onto cooling rack and let cool completely.
Beat the cream cheese until it softens, then add the powdered sugar a little at a time. Beat until very smooth and well incorporated. You may add 1 or 2 drops of milk if necessary to make it spreadable.