In a large bowl, mash your bananas. Add the eggs, one at a time, beating well after each addition. Add the brown sugar and mix well until the sugar dissolves. Add the apple sauce and vanilla extract and mix well.
Now you can add the dry ingredients except for the chopped pecans. Mix until just combined. Do not overmix.
Mix in the chopped pecans or any other nuts of your choice.
Pour the batter into the loaf pan and bake for 45-50 minutes until a cake inserter or toothpick comes out with a few crumbs on it.
Let it cool in the pan for 10-15 minutes. Then remove it and let it cool completely on a wire rack.