Preheat your oven to 350°F (175°C).
In a mixing bowl, mash the ripe bananas with a fork until smooth.
Stir the melted butter into the mashed bananas.
Mix in the baking soda and salt.
Add the sugar, beaten egg, and vanilla extract. Mix well.
Gradually add the flour, mixing until just incorporated.
Fold in the chopped walnuts.
Pour the batter into a greased loaf pan.
Bake 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.