Preheat oven to 350 degrees F.
Coat a 9 by 5-inch loaf pan with nonstick cooking spray; set aside. In a mixer, cream butter and sugar together. Then add applesauce and vanilla and beat until well blended. Add egg and egg whites and blend into mixture. In a separate bowl, sift together the flour, baking powder, and salt. With mixer on low, add 1/3 of the flour mixture and then add half of the milk; beat until combined. Add another 1/3 of the flour mixture, followed by the rest of the milk, and then the final 1/3 of the flour mixture. Scrape down the sides of the bowl and continue beating until just incorporated.
Pour batter into prepared loaf pan and bake for 1 hour or until a toothpick inserted in the center comes out clean. Allow to cool in pan for 10 minutes before slicing.