Preheat oven to 350º. In a medium bowl, combine sifted flour, baking soda, and salt. Whisk together eggs, vanilla, butter, and sugar. Prepare a loaf pan and lightly brush with butter or spray with non-stick cooking spray.
In a mixer, cream together the flour mixture with the eggs mixture. Mix until smooth then add in bananas and nuts slowly and mix until smooth which is about 2 minutes.
Transfer the batter into a loaf pan and bake for 55 minutes. Insert a toothpick into the center of the bread and if it comes out clean then the bread is ready.