Preheat oven to 375 degrees F. In large bowl of electric mixer, beat eggs, oil, and vanilla until well combined.
Combine flour, sugar, cinnamon, nutmeg, baking soda, baking powder, and salt, stirring to combine thoroughly. Add to egg mixture and stir to blend. Stir in apples and nuts.
Spoon batter into a greased 9- by 13-inch baking pan, or a 10-inch fluted or plain tube pan.
Bake until a skewer inserted in center comes out clean (30 to 40 minutes, or 40 to 50 minutes if using a tube pan). Cool 30 minutes in pan on rack before cutting.
Nutritional Information Per Serving:
357 Calories; 17 g Fat; 5 g Protein; 47 g Carbohydrate;
45 mg Cholesterol; 205 mg Sodium