Upside-down Apple Tart (Tarte Tatin)

For the pastry: Sift together flour, sugar, and salt into a large mixing bowl. Use a pastry cutter or two knives to work butter into flour until it resembles coarse meal. Stir in egg with a fork until dough just begins to hold together. Press dough into a rough ball, then transfer to a lightly floured surface. Knead dough a few times, gather into a ball, then flatten slightly to make a disk. Wrap disk in plastic and refrigerate for 30 minutes.

For the apples: Preheat oven to 375°. Peel, quarter, and core apples. Melt butter in a 10" cast-iron skillet over medium heat, then remove from heat and sprinkle evenly with sugar. Tightly pack apples around inside edge of skillet, standing upright on their sides, nestled against one another. Arrange remaining apples in similar position in center of skillet. (Apples will shrink as they cook.) Return to high heat and cook until butter and sugar caramelize to a rich brown, about 15 minutes. Remove from heat, then carefully turn apples over to uncooked side with a fork, taking care not to burn your fingers. Return to heat and cook 5-8 minutes longer. Remove from heat.

Roll out dough on a lightly floured surface into a 12" circle. Drape pastry over apples and skillet, then tuck overhanging dough between apples and inside wall of skillet. Bake in oven until pastry is golden, 20-30 minutes. Allow tart to cool for 15 minutes, then loosen edges with a knife. Place a platter on top of skillet and invert quickly and carefully. Serve warm.