In a large bowl whisk together eggs, flour, and sugar, whisking until the
mixture is smooth. Whisk in the milk, cinnamon and vanilla extract, until the
mixture is combined well. Stir in the apples.
In a 9- or 10-inch cast iron skillet melt the butter over moderate heat.
Pour the batter into the skillet, spreading the apples evenly, and bake the
cake in the middle of a preheated 375 degree F oven for 30 minutes, or until
it is puffed and begins to pull away from the sides of the skillet.