01 - Preheat the oven to 350°F (175°C).
02 - In a large mixing bowl, gently toss the banana slices with both sugars, 2 tbsp 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 flour, sugar, baking powder, and salt for the topping. Stir in milk and 1/3 cup melted butter until just combined; do not over-mix.
04 - Spoon the cobbler batter evenly over the banana mixture. Gently spread to cover most of the filling.
05 - Bake for 35-40 minutes, or until the topping is golden and a toothpick inserted into the crust comes out clean.
06 - Let cool slightly before serving. Serve warm, optionally with vanilla ice cream or whipped cream.