How to Make It
Cut a thin slice from the stem ends of the apple halves so they will stand upright. In a large bowl, toss the apple halves with the lemon juice to coat thoroughly.
Set a 12-inch flameware or cast-iron skillet over low heat. Add the butter and heat until melted. Stir in the sugar and salt and cook for 5 minutes, until the sugar has dissolved but hasn't browned.
Pack the apple halves into the skillet, standing them upright in concentric circles. Cook over moderate heat until all but the tops are softened and their juices have formed a rich caramel, about 1 hour and 15 minutes. For even cooking, rotate the skillet 45 degrees about every 10 minutes. Lightly press down the apples with a spatula as they soften. Shake the skillet occasionally to prevent the apples from sticking.
Meanwhile, preheat the oven to 400°. On a lightly floured work surface, roll out the puff pastry to a 14-inch round about 1/8 inch thick. Prick the pastry all over with a fork. Refrigerate for 10 minutes.
Drape the pastry over the apples and tuck in the edge with a spoon. Bake for about 30 minutes, until the pastry is golden brown and cooked through. Remove from the oven and carefully invert the tart onto a platter. Let cool for 10 minutes, then cut into wedges and serve.
Vanilla ice cream, whipped cream or crème fraîche.