In a blender or large bowl, mix eggs, milk, flour, sugar, vanilla, salt and cinnamon until blended. (If using an electric mixer, batter will remain slightly lumpy.)
In the oven, melt butter in a 12-inch fluted porcelain quiche dish or a 13-by 9-inch baking dish; add add apple slices and return to oven until butter sizzles. Do not let it brown. Remove dish from oven and immediately pour batter over apples. Sprinkle with brown sugar. Bake in middle of oven 20 minutes or until puffed and brown. Serve immediately.