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 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 and saucy.
03 - Remove the skillet from heat and carefully pour the banana mixture into the prepared baking dish, spreading it into an even layer across the bottom.
04 - In a medium mixing bowl, whisk together the flour, granulated sugar, baking powder, and salt. Pour in the whole milk, melted butter, and vanilla extract, then stir gently until just combined. Avoid overmixing to keep the topping tender.
05 - Spoon the batter in scattered dollops over the banana filling. Use a spatula to gently spread the topping without fully covering the fruit, leaving some areas exposed for a rustic, golden finish.
06 - Bake on the center rack for 35 to 40 minutes, or until the topping is golden brown and a toothpick inserted into the crust comes out clean.
07 - Allow the cobbler to rest for 10 to 15 minutes before serving. Serve warm, topped with vanilla ice cream or whipped cream if desired.