In large mixing bowl, beat butter until smooth. Add eggs and beat thoroughly. Then add sugar, and again beat until smooth.
In a separate bowl, combine flour, baking powder, salt, and baking soda. Mix until ingredients are thoroughly combined. Add dry ingredients to butter-egg-sugar mixture, and beat until thoroughly combined. Add the applesauce and beat again.
Fold in apple chunks and walnuts.
Grease and flour a bundt pan, or 2 small loaf pans, and fill. Bake at 350 degrees F for 45 to 50 minutes. Before serving, frost top of cake with glaze.