Preparation

Make the dough

• Put the flour, sugar, and salt in a food processor. Add the butter and vegetable shortening and pulse until the mixture resembles coarse meal, 10 to 12 pulses. Sprinkle 1/3 cup cold water over the mixture and pulse until the dough just starts to come together, 8 to 10 pulses more. If the mixture seems dry, add more water 1 tsp. at a time. Do not overprocess.

  Turn the dough out onto a clean work surface, and gather it into a rectangle that’s about 8 by 12 inches. Flatten slightly, wrap in plastic and refrigerate for at least 2 hours and up to 3 days.

Make the filling

• In a heavy-duty 4-quart saucepan, combine the dried apricots, sugar, wine, orange juice, and 2/3 cup water. Simmer over medium-low heat, stirring often, until the apricots are very tender and can be mashed with a wooden spoon, 40 to 45 minutes. Add more water if the apricots are still not soft after most of the liquid has evaporated. The mixture should get thick and syrupy; don’t let it scorch. Add the fresh apricots and lemon juice and cook, stirring often, until very soft, about 10 minutes. Mash the mixture with a wooden spoon or potato masher so that it has a thick, jam-like consistency. Remove from the heat.

  Stir 3/4 cup of the almonds, the brandy, and almond extract into the apricot mixture. Cool to room temperature and set aside. (The filling can be made, covered, and refrigerated up to 2 days ahead.)

Assemble and bake the pie

• Position a rack in the center of the oven and heat the oven to 375°F. Line a large rimmed baking sheet with parchment. In a small bowl, beat the egg yolk with 1 tsp. water.

  On a lightly floured surface with a lightly floured rolling pin, roll the dough into a 1/8-inch-thick, 12×18-inch rectangle. Be sure to loosen the dough several times and reflour underneath so that it doesn’t stick. Trim the dough into an 11×16-inch rectangle and transfer it to the baking sheet. Turn the baking sheet so that a long side faces you, and brush the edges of the dough with the egg wash. Spread the apricot filling evenly over the bottom half of the dough, leaving a 1/2-inch border. Fold the top half of the dough over the filling, pressing along the edges to secure the sides. Press lightly along the edges with the back of a fork to seal. Brush egg wash all over the top of the dough. Using a paring knife, cut 5 small steam vents in the dough at about 3-inch intervals.

  Bake until the pie is golden-brown, 55 minutes. Transfer to a rack to cool completely.

  In a small bowl, mix the confectioners’ sugar, cream, and vanilla extract to form a smooth glaze that’s just fluid enough to drizzle. With a spoon, drizzle the glaze over the top of the pie and immediately sprinkle with the remaining 1/4 cup almonds. Allow to set for at least 2 hours before serving.

  When ready to serve, use a serrated knife to cut the pie. The pie is best eaten the day it’s made, but it will keep for 1 day, well wrapped, at room temperature.