How to Make It
On a lightly floured work surface, roll out the puff pastry 1/8 inch thick. Cut out a 12-inch round, transfer to a baking sheet and refrigerate; reserve the pastry scraps for another use.
In a 10-inch cast-iron skillet, melt the butter. Add the sugar and cook over moderately low heat, stirring occasionally, until the sugar is dissolved and the mixture comes to a simmer, about 2 minutes. Remove from the heat. Arrange the apple halves standing upright in the skillet in 2 snug concentric circles. Return to the heat and cook undisturbed until an amber caramel forms, about 30 minutes.
Preheat the oven to 375°. Top the apples with the puff pastry and bake for about 40 minutes, until the pastry is golden and the apples are tender. Let cool for 15 minutes.
Place a large plate on top of the skillet and carefully invert the tart. Serve warm with crème fraîche.