FRENCH UPSIDE-DOWN APPLE PIE

Steps:

• To make the dough, whisk the salt and powdered sugar into the flour. Rub the softened butter into the flour using the tips of your fingers, until the mixture feels like moist sand. Mix the beaten egg into the flour mixture until you can form a ball. Using the palm of your hand, mash the dough into a clean pastry board a few times (a technique called "fraisage" which is similar to kneading), until the dough is smooth. Gather into a ball and flatten into a disc. You can let the dough rest in the refrigerator while you prepare your apples.
• Peel, core, and cut the apples into quarters. In a large 9 to 10-inch cast iron skillet (or other oven-proof skillet), melt the butter. Once it has melted, turn off the heat and sprinkle the sugar evenly on top of the melted butter. Place the quartered apples in a circular arrangement in the skillet, as snuggly as you can fit them, cut-side up. Put the skillet on high heat and allow the apples to simmer in the caramel for about 10 to 15 minutes. You can swish the caramel around a bit to prevent from burning and ensure the apples are cooking evenly. Occasionally spear an apple with a sharp knife and make sure the bottom isn't burning or sticking to the pan. You can scoop some of hot caramel and drizzle it on the tops of the apples if you wish. Once the caramel begins to turn slightly amber in color, immediately remove the skillet from the heat. The apples will have shrunk slightly and with a fork, you can gently bring them as close together as you can, shrinking your overall circle. Leave them to cool slightly while you roll out your pastry.
• On a lightly floured surface, roll out the pastry dough to about 1/8 inch thick. Place the dough over the apples and cut off any excess amounts, leaving a 1-inch overhang. Tuck the dough in around the outer edges of the apples. Make a few slits on top of the dough, to allow the steam to vent.
• Bake the pie in a 375 F oven, for about 30 minutes, until the top of the pie is golden.
• Do not wait more than 10 minutes before flipping your pie over onto a serving plate. The apples must still be hot when you invert the pie otherwise the caramel will harden and the apples may stick to the skillet. Before inverting, first run a sharp knife along the inner edge of the skillet to separate any dough that has stuck to the side. Gently shake your skillet from side to side to loosen any apples that may be stuck. Using oven mitts and a plate that is wider than the top rim of your skillet, hold the plate tightly against the skillet and flip them over in one swift motion. Gently lift the skillet and if any apples have remained behind, simply loosen them and place them back in their spots. Serve warm.