01 - Preheat oven to 350°F. Grease an 8-inch square baking dish with butter or nonstick cooking spray and set aside.
02 - Melt 2 tablespoons of unsalted 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 medium mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt. Pour in the whole milk, melted butter, and vanilla extract, then stir until just combined. Be careful not to overmix, as a slightly lumpy batter produces a more tender topping.
04 - Spoon the batter in generous dollops over the banana filling. Use a spatula to gently spread the batter, leaving some gaps exposed for a rustic, golden finish as it bakes.
05 - Place the dish on the center rack and 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. Spoon warm portions into bowls and top with vanilla ice cream or whipped cream if desired.