Preheat oven to 350°. Grease a 9x5 loaf pan and set aside.
In a mixing bowl, combine together eggs, applesauce, apple cider, pumpkin, and sugars. Mix until just combined.
Add flour, baking powder, baking soda, salt, cinnamon, cloves, and nutmeg to wet ingredients. Mix until combined.
Stir in apples and walnuts. Pour batter into loaf pan and bake 55-60 minutes or until toothpick comes out clean. Let cool 15 minutes before removing from pan. Store on the counter for 2 days or in refrigerator for up to 1 week.