Preheat oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a large bowl, mash the overripe bananas with a fork until smooth.
Whisk the melted butter into the mashed bananas, then whisk in the sugar, egg, and vanilla extract until completely combined.
Sprinkle the baking soda and salt over the wet mixture. Gently fold in the flour using a spatula, stopping as soon as no dry streaks remain to avoid overmixing.
Divide the batter evenly into the muffin cups, filling them about 3/4 full.
Bake for 18-22 minutes, or until a toothpick inserted into the center comes out clean. Cool in the pan for 5 minutes before transferring to a wire rack.