Preheat your oven to 350°F (175°C). Grease a 9×5-inch loaf pan with butter or non-stick spray.
In a large mixing bowl, combine the mashed bananas and melted butter. Stir until smooth.
Add the granulated sugar, beaten egg, and vanilla extract to the banana mixture. Mix well until fully combined.
Sprinkle the baking soda and salt over the mixture and stir to incorporate.
Add the all-purpose flour last, mixing gently until just combined. Do not overmix to keep the bread tender.
Pour the batter into the prepared loaf pan and spread evenly.
Bake in the preheated oven for 60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the banana bread from the oven and let it cool in the pan for 10 minutes.
Transfer the bread to a wire rack and allow it to cool completely before slicing and serving.