01 - Preheat oven to 350°F. Grease an 8-inch square baking dish with butter or non-stick 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 syrupy. Remove from heat and spread the filling evenly across the bottom of the prepared baking dish.
03 - In a mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt. Pour in the whole milk, melted butter, and vanilla extract, then stir until just combined. Avoid overmixing to keep the topping tender.
04 - Spoon the batter in generous dollops over the banana filling. Use a spatula to gently spread it, leaving some gaps exposed so the filling bubbles through for a rustic, golden finish.
05 - Bake for 35 to 40 minutes, or until the cobbler topping is 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. Scoop warm into bowls and top with vanilla ice cream or whipped cream if desired.