01 - Preheat the oven to 350°F. Grease an 8-inch square baking dish with butter or nonstick spray and set aside.
02 - In a large skillet, melt 2 tablespoons of butter 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 thick and 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 flour, granulated sugar, baking powder, and salt. Pour in the 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 for a rustic, golden finish as it bakes.
05 - Bake for 35 to 40 minutes, or until the topping is deep golden brown and a toothpick inserted into the crust comes out clean.
06 - Allow the cobbler to cool for 10 to 15 minutes before serving. Scoop into bowls while still warm and top with vanilla ice cream or whipped cream if desired.