01 - Preheat your oven to 350°F. Lightly grease an 8-inch square baking dish with butter or nonstick spray.
02 - In a large mixing bowl, gently toss the sliced bananas with the granulated sugar, brown sugar, 2 tablespoons melted butter, lemon juice, cinnamon, nutmeg, salt, and vanilla extract until evenly coated. Spread the mixture in an even layer across the bottom of the prepared baking dish.
03 - In a separate bowl, whisk together the flour, sugar, baking powder, and salt. Pour in the milk and 1/3 cup melted butter, stirring gently until just combined. Avoid overmixing to keep the topping tender.
04 - Spoon the batter in even dollops over the banana filling, then gently spread it with a spatula to cover most of the surface. Some fruit peeking through is perfectly fine.
05 - Bake for 35 to 40 minutes, or until the cobbler topping is golden brown and a toothpick inserted into the crust comes out clean.
06 - Allow the cobbler to rest for 5 to 10 minutes before serving. Serve warm on its own or topped with a scoop of vanilla ice cream or a dollop of whipped cream.