Preheat oven to 350. Grase and flour a 9x5 inch loaf pan.
Combine the dry ingredients in a large bowl and set aside.
In a separate bowl, mash the bananas, add the eggs, oil, applesauce and vanilla. Mix thoroughly.
Add the wet ingredients to the dry and mix well. The batter will be thick and more oil, applesauce or some buttermilk can be added if it is too dry for your liking.
Pour batter into the prepared pan and bake for 45-50 minutes, or until the loaf is firm to the touch. Remove form oven and cool for 5 minutes, then remove the bread and cool on a wire rack for 10 minutes.