01 - Preheat 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 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, granulated sugar, baking powder, and salt. Pour in the whole milk and 1/3 cup melted butter, stirring gently until just combined. Be careful not to overmix—a few lumps are fine.
04 - Spoon the batter evenly over the banana filling, using a spatula to gently spread it across the surface. The batter does not need to cover every inch; it will spread as it bakes.
05 - Bake on the center rack for 35 to 40 minutes, until the topping is 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 fresh whipped cream.