Preheat the oven to 350°F (175°C). Grease a 9×5 inch loaf pan or line it with parchment paper.
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 combined.
Sprinkle the baking soda and salt over the mixture and stir to incorporate.
Add the all-purpose flour last and gently fold it into the wet ingredients until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and spread it 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 to cool completely before slicing and serving.