Preheat oven to 425 F. In a blender or large bowl, mix eggs, milk, flour, sugar, vanilla, salt and cinnamon until blended (batter will be lumpy).
Melt butter in a 12" quiche dish or a 13x9 baking dish. Add apple slices to baking dish. Return to oven until butter sizzles - do not let brown. Remove from oven and pour batter over apples. Sprinkle with brown sugar. Bake for 20 minutes in the middle of the oven. Serve immediately.