Peel the ripe bananas and mash them thoroughly in a bowl using a fork until smooth.
Whisk the melted butter, white sugar, beaten eggs, and vanilla extract into the mashed bananas until fully combined.
Gently fold in the all-purpose flour, baking soda, and salt with a spatula just until no dry flour spots remain.
Pour the smooth batter into a greased and parchment-lined 8x4-inch loaf pan, smoothing the top evenly.
Bake at 350°F (175°C) for 55 to 60 minutes until a toothpick inserted into the center comes out clean, then cool before slicing.