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