Preheat your oven to 350°F (175°C).
In a mixing bowl, mash the bananas until smooth.
Add the softened butter and mix well.
Stir in the sugar, eggs, and vanilla extract.
In another bowl, combine the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the banana mixture, stirring 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.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.