Wash, peel, and core the apples. Slice them into ¼-inch thick slices. Add the sliced apple, brown sugar, flour, lemon juice, cinnamon, nutmeg, vanilla, and salt to a large bowl. Use your hands to gently combine everything so the apples are well-coated. Let the apples sit at room temperature until they form a syrupy liquid in the bottom of the bowl, about 1 hour.
MAKE THE TOPPING:
Whisk together the butter, milk, and vanilla in a large bowl. Whisk in the flour, sugar, baking powder, and salt until combined.
ASSEMBLE AND BAKE THE COBBLER:
Preheat the oven to 350 degrees F. Spray the inside of a 9x13-inch baking dish with nonstick spray.
Pour the filling (including the syrupy liquid at the bottom of the bowl) into the prepared baking dish. Pour the topping onto the apple filling.
Bake until the top is golden, and a toothpick inserted into the cake portion comes out clean, about 45 to 55 minutes. Serve warm, topped with a scoop of vanilla ice cream if desired.