Preheat your oven to 350°F (175°C). Grease a 4x8 inch loaf pan.
In a mixing bowl, mash the ripe bananas with a fork until smooth. Stir in the melted butter.
Mix in the baking soda and salt.
Add the sugar, beaten egg, and vanilla extract. Stir until well combined.
Gradually mix in the flour until just incorporated. Be careful not to overmix.
If using, fold in the chopped walnuts.
Pour the batter into the prepared loaf pan.
Bake for 60-65 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.