Preheat your oven to 350°F (175°C). Lightly grease a baking dish with butter or nonstick spray.
In a large bowl, gently combine the sliced bananas, sugar, melted butter, vanilla extract, cinnamon, and salt. Let the mixture rest for a few minutes so the flavors blend.
In a separate bowl, whisk together the self-rising flour, whole milk, sugar, and nutmeg until just combined. A few small lumps are perfectly fine.
Pour the batter into the prepared baking dish without stirring.
Spoon the banana filling evenly over the batter. Do not mix. As it bakes, the layers will create the classic texture of Southern Banana Cobbler.
Bake for 45 to 50 minutes, or until the top is golden brown, the filling is bubbly, and the center is set.
Let the cobbler cool for about 10 minutes before serving.
Serve warm with vanilla ice cream, whipped cream, chopped nuts, or caramel drizzle if desired.