- Preheat oven to 350° F. 
- Cream butter and sugar in a large mixing bowl. Add cinnamon, nutmeg, vanilla, and salt. 
- Combine flour and baking soda; add milk alternately with flour and baking soda mixture, mixing until all ingredients are incorporated. 
- Stir in grated apple. 
- Pour into a greased 9x13 inch pan. Bake for 40-45 minutes, until toothpick inserted in the center comes out clean. 
- Place cake on a rack to cool. 
- Once cool, prepare frosting by combining butter, cream cheese, and vanilla in a large mixing bowl. Use a hand mixer to beat until smooth (about one minute). Add powdered sugar and beat until smooth, then beat 1-2 more minutes.