01 - Preheat oven to 350°F. Grease an 8-inch square baking dish with butter or nonstick spray and set aside.
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 thick and 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, then stir until just combined. Be careful not to overmix, as a slightly lumpy batter produces the best texture.
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 topping comes out clean.
06 - Allow the cobbler to cool for 10 to 15 minutes before serving. Serve warm, optionally topped with a scoop of vanilla ice cream or a dollop of freshly whipped cream.