Preheat oven to 350 degrees F(175 degrees C). Grease and flour a 9x13 inch pan.
Chop apples finely and place into a large bowl. In a separate bowl, beat eggs and oil together and pour over apples. Let stand while mixing the dry ingredients.
in a medium bowl, mix sugar, flour, 1 teaspoon salt, cinnamon, nutmeg and baking soda. Fold into apples, eggs and oil and mix well. Batter will be thick.
Pour into prepared 9x13 inch pan, and bake at 350 degrees F ( 175 degrees C) for 45 minutes. Once cool frost with Cream Cheese Icing.
To Make Cream Cheese Frosting: In a medium bowl, combine cream cheese, milk, vanilla and pinch of salt. Gradually add sugar, beating until frosting is smooth. Add additional milk, 1 tablespoon at a time, until frosting is desired consistency.
