01 - Preheat the oven to 350°F. Grease a 9-inch square or round baking dish with softened butter, coating the bottom and sides evenly.
02 - In a large bowl, gently toss the sliced bananas with granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, cornstarch, and vanilla extract until the slices are evenly coated. Spread the mixture in 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 melted butter and milk, stirring just until a thick, pourable batter forms. Avoid overmixing to keep the topping tender.
04 - Spoon the batter over the banana filling, spreading gently to cover most of the fruit surface. Sprinkle with coarse sugar for a crisp, caramelized top if desired.
05 - Bake for 35 to 40 minutes, until the topping is deep golden brown and the filling is actively bubbling around the edges of the dish.
06 - Let the cobbler rest for at least 10 minutes before serving warm. Pair with vanilla ice cream or whipped cream for a classic presentation.