Slice the bananas into pieces about 1/4 inch thick.
In a large bowl, gently combine the sliced bananas with granulated sugar, brown sugar, melted butter, water, lemon juice, vanilla extract, ground cinnamon, ground nutmeg, and a pinch of salt.
Allow the banana mixture to rest for approximately 15-20 minutes.
In another large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, and salt.
In a separate small bowl, whisk together the cold buttermilk, melted and slightly cooled butter, and vanilla extract.
Pour the wet mixture into the dry ingredients and stir until just blended, being careful not to overmix.
Preheat your oven to 375°F (190°C).
Transfer the banana filling to a 9x13 inch baking dish.
Gently pour the cobbler topping over the banana filling.
If desired, sprinkle turbinado sugar over the top of the cobbler.
Bake in the preheated oven for 35-45 minutes, or until the topping is golden brown and a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Once baked, remove the cobbler from the oven and allow it to cool for at least 15-20 minutes before serving.
Serve warm, topped with whipped cream or vanilla ice cream, if you like.
