HOW TO MAKE IT

1. Make the dough: Place the flour in a large bowl and make a well in the center. Add the sugar, salt, and egg yolk and mix slowly with your hands. Add the butter and mix until you have a smooth and homogenous dough. Form the dough into a ball, cover with plastic wrap, and refrigerate for at least 1 hour or overnight.
2. Preheat the oven to 350°F. Butter a 10-inch cast-iron fry pan.
3. Prepare the apples: In a medium bowl, mix the sugar with the vanilla bean seeds. Sprinkle the vanilla sugar over the bottom of the skillet, scatter the butter over the sugar, then tightly pack the apples in the pan in a circular fashion, with one flat side down.
4. Set the fry pan over medium-high heat and cook until the apple liquid starts to bubble, about 3 minutes. Reduce the heat and continue to cook until the juices turn a golden caramel color, about 10 minutes. Remove from the heat.
5. On a lightly floured work surface, roll out the dough 1⁄8 inch thick. Using a sharp knife, cut a round of dough just slightly larger than the top of the fry pan. Drape the dough over the apples to cover them and carefully use your fingers to tuck the dough between the pan and the apples all around. Transfer to the oven and bake until the pastry is golden brown, about 40 minutes.
6. Remove from the oven and let cool for 5 minutes. Carefully unmold the tatin by placing a large serving plate on top of the pan and inverting the cake onto the plate. Serve with crème fraîche.