Preheat your oven to 350°F (175°C). Grease a 9x9 inch baking dish.
In a large bowl, mash the ripe bananas. Add the melted butter, granulated sugar, vanilla extract, and egg. Mix until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour the banana bread batter into the prepared baking dish and spread evenly.
To make the cobbler topping, in a medium bowl, combine the flour, brown sugar, and cinnamon. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Sprinkle the cobbler topping evenly over the banana bread batter.
Bake for 40-50 minutes, or until the topping is golden brown and a toothpick inserted into the center comes out clean.
Let cool slightly before serving. Serve warm, perhaps with a scoop of vanilla ice cream.
Notes
This cobbler is best served warm. You can add chocolate chips or chopped nuts to the batter for extra flavor.