Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the mashed bananas and melted butter.
Add sugar, eggs, and vanilla extract, and mix until well combined.
In a separate bowl, whisk together flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring gently.
If desired, fold in chopped nuts.
Pour the batter into a greased 9x5 inch loaf pan.
Bake for 60-65 minutes, or until a toothpick comes out clean.
Remove from the oven and allow to cool in the pan for 10 minutes.
Transfer the bread to a wire rack to cool completely.
