Step 1Melt the butter in a 12-inch cast-iron or heavy skillet over medium-high heat. Remove from the heat and sprinkle in the sugar. Stir until the butter is evenly mixed in.
Step 2Working clockwise, tightly pack the apple wedges around the inside edge of the skillet, laying them on their sides. The apples will shrink as they cook, so don't hesitate to pack them tight. With the remaining apples, arrange them on their sides in the center of the skillet.
Step 3Cook the apples over high heat until the butter and sugar turn brown and caramelize, about 10 minutes. Turn off the heat and carefully turn the apples over to the uncooked side using 2 forks. Make sure that the apples are browned before you turn them over. Pack the apples tightly on their sides. If you see a loose area, rearrange the apples a bit to fill in the gap. Return to high heat and cook for another 5 minutes. Turn off the heat and let the apples cool in the skillet while you work on the dough.
Step 1Sift together the flour, powdered sugar and salt onto a flat surface. Make a well in the sifted ingredients for the butter. Using a pastry cutter, cut the butter into the flour mixture until it resembles a lumpy coarse meal. Stir in the egg and quickly work it into the flour mixture until it holds together. Pat and press the dough into a disk. Wrap the dough with plastic and refrigerate for at least 30 minutes.
Step 2Heat the oven to 375 degrees.
Step 3Once the dough has chilled, lightly flour a flat surface and a rolling pin. Roll out the dough into a circle slightly larger than the skillet. Lay the dough over the apples and tuck the extra dough between the apples and the side of the skillet. Trim off excess dough.
Step 4Bake until the pastry is golden, 30 to 35 minutes. Allow the tart to cool in the skillet for 15 minutes. With a sharp knife, cut around the edges. Carefully, turn the hot tart over onto a large serving platter. Serve warm.