Preheat your oven to 350°F (175°C). Grease a 9x5 inch loaf pan.
In a mixing bowl, mash the ripe bananas with a fork or potato masher until smooth.
Stir in the melted butter.
Add the sugar, beaten egg, and vanilla extract. Mix well.
Sprinkle the baking soda and salt over the mixture and stir until evenly combined.
Gradually add the flour, stirring until just incorporated. Be careful not to overmix.
If using, fold in the chopped nuts.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the banana nut bread to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.