Preheat oven to 350°F (175°C). Grease a 9x5 inch loaf pan.

In a bowl, mash the bananas with a fork until smooth. Add melted butter, sugar, beaten egg, and vanilla extract. Mix well.

In a separate bowl, whisk together the baking soda, salt, and flour.

Gradually add the dry ingredients to the wet mixture, mixing until just combined.

Pour the batter into the prepared loaf pan.

Bake for 60 minutes, or until a toothpick inserted into the center comes out clean.

Let the banana bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.