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, beaten egg, and vanilla extract until well combined.

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 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.

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