Preheat & prep
Heat the oven to 350°F (175°C). Grease a 9×9-inch baking dish (or a similar-size oven-safe pan).

Make the banana filling
Melt the butter in a large skillet over medium heat. Add the banana slices and sauté 3–4 minutes, until they soften and begin to brown. Stir in the brown sugar, vanilla, cinnamon, nutmeg, and a pinch of salt. Cook another 2–3 minutes until the sugar melts and the mixture becomes saucy. If using rum, carefully pour it in and let it bubble for 1–2 minutes. Remove from heat and spread the warm mixture evenly in the prepared dish.

Prepare the cobbler topping
In a medium bowl, whisk together the flour, baking powder, granulated sugar, and salt. Add the cold cubed butter and cut it into the dry mix with a pastry cutter or your fingertips until the mixture looks like coarse crumbs with pea-sized bits of butter. Stir in the buttermilk and vanilla just until the dough comes together — it should be slightly sticky.

Assemble and bake
Spoon dollops of the topping over the banana filling, distributing them so the fruit peeks through here and there. Bake for 25–30 minutes, until the top turns golden and a toothpick inserted into the center comes out clean.

Cool & serve
Let the cobbler rest 5–10 minutes before scooping. The pause helps the filling thicken a touch for easier serving.