01 - Preheat the oven to 350°F. Grease a 9-inch square or round baking dish with the 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 evenly coated. Spread the mixture across the prepared baking dish in a uniform layer.
03 - In a separate bowl, whisk together the flour, granulated 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 coarse sugar evenly over the top if a crunchy crust is desired.
05 - Bake for 35 to 40 minutes, until the topping is deep golden brown and the filling is bubbly around the edges.
06 - Let the cobbler cool for at least 10 minutes before serving warm. Pair with vanilla ice cream or whipped cream for a classic finish.