Heat the oven to 350 degrees Fahrenheit and spray the loaf pan with cooking spray.
Combine the whole wheat flour, baking powder, baking soda, salt, oats and cinnamon in a bowl.
Mix together in a second bowl the applesauce, egg substitute and grated apple.
Stir the flour mixture into the applesauce mixture until combined.
Fold the toasted walnuts into the batter and pour the mix into the loaf pan.
Bake at 350 degrees Fahrenheit for 35 to 45 minutes or until a knife comes out cleanly from the center. Let it cool completely before slicing and serving.