Preheat oven to 350°F (175°C). Grease a 9x5 inch loaf pan or line with parchment paper.
In a large bowl, mash the bananas with a fork until smooth.
Stir in the melted butter.
Mix in the sugar, beaten egg, and vanilla extract.
Sprinkle in the baking soda and salt. Stir to combine.
Fold in the flour until just combined. Do not overmix — a few lumps are fine.
Fold in walnuts or chocolate chips if using.
Pour the batter into the prepared loaf pan and bake for 55–65 minutes, until a toothpick inserted in the center comes out clean.
Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.
Notes
Use deeply speckled, very ripe bananas for the best flavor. Don't overmix the batter or the loaf will be tough. Ovens vary — start checking at 55 minutes.