01 - Preheat the oven to 350°F. Grease a 9-inch square or round baking dish with the softened butter.
02 - In a large bowl, gently toss the sliced bananas with granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, cornstarch, and vanilla extract until evenly coated. Spread the mixture 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 melted butter and milk, stirring until just combined into a thick, pourable batter. Take care not to overmix.
04 - Spoon the batter over the banana filling, spreading gently to cover most of the fruit. Sprinkle with coarse sugar if a crunchy top is desired.
05 - Bake for 35 to 40 minutes, until the topping is golden brown and the filling is bubbly around the edges.
06 - Let the cobbler rest for at least 10 minutes before serving warm. Pair with vanilla ice cream or whipped cream for a classic finish.