Preheat the oven to 350°F (175°C). Grease a loaf pan.

In a mixing bowl, mash the ripe bananas with a fork until smooth.

Stir in the melted butter into the mashed bananas.

Mix in the beaten egg and vanilla extract.

In another bowl, whisk together the flour, sugar, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the chopped walnuts if using.

Pour the batter into the prepared loaf pan.

Bake in the preheated oven for 60 minutes, or until a toothpick inserted into the center comes out clean.

Allow to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.