In a large mixing bowl, mash the ripe bananas until smooth.
Add the melted butter, milk, egg, and vanilla extract to the mashed bananas and mix well until combined.
In a separate bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Prepare a 7-inch round cake pan or heatproof dish that fits inside a large pot with a lid. Grease the pan with butter or line it with parchment paper.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Fill a large pot with about 2 inches of water and bring it to a simmer over medium heat.
Place a steaming rack or heatproof stand inside the pot, making sure the water does not touch the bottom of the cake pan.
Carefully place the cake pan on the rack inside the pot. Cover the pot with a tight-fitting lid.
Steam the cake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean. Check the water level occasionally and add more hot water if necessary to maintain the level.
Once cooked, carefully remove the cake pan from the pot and allow the cake to cool in the pan for 10 minutes.
Remove the cake from the pan and transfer it to a wire rack to cool completely before serving.