01 - Preheat your oven to 350°F.
02 - In a large mixing bowl, gently toss the banana slices with granulated sugar, brown sugar, 2 tablespoons melted butter, lemon juice, cinnamon, nutmeg, salt, and vanilla. Spread the mixture evenly into a greased 8-inch square baking dish.
03 - In a separate bowl, combine the flour, sugar, baking powder, and salt. Stir in the milk and 1/3 cup melted butter until just combined; do not over-mix.
04 - Spoon the cobbler batter evenly over the banana mixture and gently spread to cover as much of the filling as possible. Bake for 35 to 40 minutes, or until the topping is golden brown and a toothpick inserted into the crust comes out clean.
05 - Allow the cobbler to cool slightly before serving. Serve warm, optionally topped with vanilla ice cream or whipped cream.