01 - Preheat oven to 350°F. Grease an 8-inch square baking dish with butter or nonstick spray.
02 - Melt 2 tablespoons of butter in a large skillet over medium heat. Add the sliced bananas, granulated sugar, brown sugar, cinnamon, nutmeg, vanilla extract, lemon juice, and a pinch of salt. Cook for 3 to 5 minutes, stirring gently, until the bananas soften and the mixture becomes saucy. Remove from heat and spread the filling evenly across the bottom of the prepared baking dish.
03 - In a medium mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt. Pour in the milk, melted butter, and vanilla extract, stirring until just combined. Avoid overmixing to keep the topping tender.
04 - Drop spoonfuls of batter over the banana filling, spreading gently with a spatula. Leave some gaps exposed to allow steam to escape and create a rustic, golden finish.
05 - Bake for 35 to 40 minutes until the topping is deep golden brown and a toothpick inserted into the crust comes out clean.
06 - Allow the cobbler to rest for 10 to 15 minutes before serving. Serve warm, optionally topped with a scoop of vanilla ice cream or a dollop of whipped cream.