Preheat your oven to 350°F (175°C).
In a mixing bowl, mash the bananas until smooth.
Add the melted butter to the mashed bananas and mix well.
Mix in the sugar, beaten eggs, and vanilla extract.
Combine the flour, baking soda, and salt in a separate bowl. Gradually add to the banana mixture, stirring until just combined.
Pour the batter into a greased baking pan.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.