01 - Preheat oven to 350°F. Grease an 8-inch square baking dish with butter or non-stick spray.
02 - In a large mixing bowl, gently toss the sliced bananas with granulated sugar, brown sugar, 2 tablespoons melted butter, lemon juice, cinnamon, nutmeg, salt, and vanilla extract until evenly coated. Spread the mixture into the prepared baking dish in an even layer.
03 - In a separate bowl, whisk together the flour, granulated sugar, baking powder, and salt. Pour in the whole milk and 1/3 cup melted butter, stirring gently until just combined. Avoid over-mixing to keep the topping tender.
04 - Spoon the batter evenly over the banana filling, spreading gently to cover most of the surface. Do not worry about perfect coverage — the batter will spread as it bakes.
05 - Bake for 35 to 40 minutes until the cobbler topping is deep golden brown and a toothpick inserted into the crust comes out clean.
06 - Allow the cobbler to cool for 10 to 15 minutes before serving. Serve warm on its own or topped with vanilla ice cream or freshly whipped cream.