Preheat oven to 350°F (175°C) and grease a 9x5 inch loaf pan.
In a large mixing bowl, mash the bananas with a fork until smooth.
Stir the melted butter into the mashed bananas.
Whisk in the brown sugar, egg, and vanilla extract until fully incorporated.
Stir in the baking soda and salt.
Gently fold in the flour using a spatula until no streaks remain.
Transfer the batter into the prepared loaf pan and smooth the top.
Bake for 60 minutes or until a tester inserted in the center comes out clean.
Let cool in the pan for 10 minutes then transfer to a wire rack to cool completely.