Preheat the oven to 350°F (175°C)
Grease and flour a cake pan
Mash ripe bananas in a bowl
Cream butter and sugar together
Add eggs and vanilla extract
Mix in the mashed bananas
Combine flour, baking powder, baking soda, and salt in another bowl
Add the dry ingredients to the wet ingredients
Mix until just combined
Pour the batter into the prepared pan
Bake for 30 to 40 minutes
Check doneness with a toothpick
Let the cake cool in the pan for a few minutes
Transfer the cake to a wire rack to cool completely
Frost or serve as desired