Preheat oven to 350° and butter/spray a 4x8-inch load pan
In a bowl, mash the bananas until smooth (I use a potato masher). Stir in the melted butter into the mashed bananas.
Mix in the baking soda, salt, sugar, vanilla extract and applesauce. Once combined, add flour.
Pour batter into loaf pan. Bake for 1 hour, to 1 hour and 10 minutes at 350°. Insert a tester and it should come out clean.
Remove from oven and let cool completely on a baking rack.
The real trick to making a quality banana bread is to make sure that the banana are as overripe as you can possibly find. Without that, your bread will just taste sweet - without much of a banana flavor. I prefer to freeze my overripe bananas and then thaw them when needed - they puree very easily and require little effort.