Preheat your oven to 350°F (175°C) and grease a 9x5 inch loaf pan.
In a large mixing bowl, combine the mashed bananas with the melted butter.
Mix in the sugar, beaten eggs, and vanilla extract until well combined.
In another bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, stirring just until combined.
Pour the batter into the prepared loaf pan.
Bake for about 60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.