Preheat the oven to 425°F Combine the flour, sugar, 1/4 teaspoon of the cinnamon and the salt in a large bowl. Make a well in the center and add the eggs, milk and vanilla. Whisk briefly to form a thin batter. (There will be lumps). Set aside.
Place the butter in a 9 x 13-inch baking dish and put the dish in the oven for 5 minutes to melt the butter. Arrange the apples slices in overlapping rows over the bottom of the dish.
Return the dish to the oven and bake until the apples are slightly softened, 10 to 12 minutes.
Pour the batter over the apples and sprinkle the top with brown sugar and the remaining 1/4 teaspoon cinnamon. Bake until puffed and browned, 20 to 25 minutes. Cool for 10 minutes before serving.