Preheat oven to 350°F. Spray two 8x5 inch nonstick loaf pans with baking spray.

In a medium bowl, combine the flour, baking soda and salt with a wire whisk. Set aside.

In a large bowl cream butter and sugar with an electric mixer. Add egg whites, bananas, apple sauce and vanilla, and beat at medium speed until thick. Scrape down sides of the bowl.

Add flour mixture and walnuts (if using), then blend at low speed until combined. Do not over mix.

Pour batter into loaf pans and bake on the center rack for 45 to 50 minutes, or until a toothpick inserted in the center comes out clean.

Let the pan cool at least 20 minutes to bring it to room temperature before slicing.