Preheat the oven to 400.Make the batter: Sift the flour, granulated sugar, cinnamon and salt into a bowl.
In a separate bowl, whisk the eggs, egg yolk, and milk until well blended.
Add about one-third of the egg mixture to the flour mixture and whisk to form a paste, then gradually incorporate the remaining egg mixture.
Whisk until well blended.
Cook the apples: With the tip of a knife, scrape the vanilla bean seeds from the pod into an ovenproof 10-inch cast-iron or stainless-steel skillet.
Add the pod and the butter and cook over moderately high heat until the butter turns nut brown.
Add the apple and cook, stirring often, for about 3 minutes to soften them.
Remove the vanilla bean pod and discard.
Sprinkle the apples with the granulated sugar, reduce the heat to moderately low, and cook until the apples are about three-fourths done and the sugar has melted and is coating the apples in a light syrup.
Add the grappa or other brandy, swirl the pan briefly, then spread the fruit evenly in the pan.
Remove the pan from the heat.
Working quickly, pour the batter through a sieve evenly over the fruit.
Bake until the edges of the clafouti are puffed and browned and the center is set, about 15 minutes.
Remove from the oven.
Put some confectioners' sugar in a sieve and generously dust the surface of the clafouti.
Serve warm directly from the pan with a dollop of crème fraîche.