Preparation

Make the crust:

• In a food processor, combine the flour, sugar, and salt, and pulse to combine. Add the butter and shortening and pulse until the mixture resembles coarse meal, about 1 minute. Transfer the mixture to a large bowl.

  Fill a measuring cup with 1/2 cup very cold water. While tossing and stirring the flour mixture with a fork, add the water 1 Tbs. at a time until the dough just begins to come together in small clumps and holds together when you pinch a little between your fingers (you may need only 1/4 cup of water).

  Transfer the dough to a clean work surface and gather it together with your hands. Lightly knead the dough once or twice, divide it in half, and shape the halves into disks. Wrap the disks separately in plastic and refrigerate for at least 1 hour or up to 2 days.

Prepare the filling:

• Position a rack in the center of the oven and heat the oven to 375°F. In a large mixing bowl, combine the rhubarb, strawberries, sugar, all the tapioca, orange juice, zest, cinnamon, clove, allspice, and salt. Toss gently to mix well, and then let sit for at least 10 minutes and up to 30 minutes (while you roll out the bottom crust).

Assemble the pie:

• If the dough was refrigerated for several hours or overnight, let it sit at room temperature until pliable, about 20 minutes. On a lightly floured surface, roll out one of the dough disks into a 1/8-inch-thick circle, 12 to 13 inches in diameter, and transfer it to a 9-inch Pyrex pie plate. Pour the filling into the pie shell and dot the top with the cold butter. In a small bowl, beat the egg yolk with 1 tsp. water. Brush the edges of the pie shell with some of the egg glaze.

  Roll out the second dough disk as above and set it over the fruit filling to form a top crust. Press the edges of the dough together to seal the crust, trim the overhang to 1/2 inch, and fold it under. Flute or crimp the dough all around. Brush the top crust with the remaining egg glaze (you won’t need all of it). Cut four 1- to 1-1/2-inch-long steam vents in the top crust.

  Set the pie on a foil-lined rimmed baking sheet and bake until the pastry is golden brown and the fruit juices bubble thickly out of the pie, 70 to 80 minutes. Transfer to a rack and let cool completely before serving, about 4 hours.