Preheat oven to 325°F.
Spray an 8-inch loaf pan with cooking spray or grease with vegetable oil and set aside.
In a large bowl, sift together flour, salt, baking soda, baking powder, cinnamon and nutmeg.
In a separate bowl, whisk together egg, oil, applesauce, yogurt, sugar and vanilla.
Add flour mixture to egg mixture and stir until well combined.
Fold in zucchini and walnuts then transfer batter to prepared pan.
Bake until risen, deep golden brown and a toothpick inserted in the middle comes out clean, 50 to 60 minutes.
Cool in pan on rack for 30 minutes then remove bread from pan and continue cooling on rack.