Preheat your oven to 350°F (175°C).
In a mixing bowl, mash the ripe bananas until smooth.
In a separate bowl, combine flour, sugar, baking powder, and salt.
Melt the butter and let it cool slightly, then mix it with the milk and vanilla extract.
Gradually add the wet mixture to the dry ingredients, stirring until just combined.
Pour half of the batter into a greased baking dish, followed by the mashed bananas, topped with the remaining batter.
Sprinkle cinnamon on top if desired, and bake for 35-40 minutes.
Let the cobbler cool for 10 minutes before serving.