Make the pastry: combine flour and a pinch of salt in a bowl. Work in the cold cubed butter until the mixture resembles coarse crumbs. Add the egg yolk and ice water, mixing until the dough just comes together. Form into a disc, wrap in plastic, and refrigerate for at least 30 minutes.

Cook the apples: melt 1/2 cup butter with sugar in a 9 to 10 inch cast-iron skillet over medium heat, stirring until dissolved. Add the vanilla. Arrange apple halves cut-side up in the skillet, packing them tightly.

Cover the skillet with foil and cook over medium heat for 20 to 30 minutes until the apples release their juices and begin to soften.

Remove apples with a slotted spoon to a cooling rack. Continue cooking the liquid in the skillet until it thickens into a golden caramel. Sprinkle fleur de sel over the cooled apples.

Preheat oven to 430°F (220°C). Return apples to the skillet, arranging them neatly. Roll out the chilled pastry into a circle slightly larger than the skillet. Drape it over the apples, tucking the edges down inside the pan.

Bake for 20 to 25 minutes until the pastry is golden brown and the caramel is bubbling around the edges. Cool for 5 minutes, run a knife around the edge, then carefully invert onto a serving plate. Serve warm with crème fraîche.