TOURTIèRE

Steps:

• Make the dough. In a food processor, pulse together the flour and salt. Add butter and lard in stages, pulsing until the mixture forms bean-size pieces. Slowly add ice water, 1 tablespoon at a time, and pulse until the dough just comes together. It should be moist but not wet.
• Turn dough out onto a lightly floured surface, and gather into two balls. Flatten each into a disk with the heel of your hand. Cover tightly with plastic wrap, and refrigerate for at least 1 hour and up to 2 days.
• Make the pork shoulder. Season the pieces of pork aggressively with salt and pepper. Put 1 tablespoon of the oil into a large, deep skillet or Dutch oven, and set it over medium-high heat. When the oil shimmers, sear the meat on all sides until browned, turning as necessary, 10 minutes.
• Add the allspice berries and cinnamon sticks, and stir to toast them, then add the beer. Bring to a boil, then reduce the heat, cover the pan and simmer steadily until the pork is very tender, 45 minutes to an hour. (When the pork is done, you can allow it to cool in its liquid and refrigerate it for one or two days before using.)
• Make the chicken or turkey. Heat oven to 325. Season the chicken or turkey thighs aggressively with salt and pepper, then roast in a cast-iron pan or shallow baking tray until their skin is crisp and they have cooked through, approximately 1 hour. (The chicken or turkey, too, may be made ahead and stored in the refrigerator before using.)
• Make the pie filling. Melt the butter in a large, heavy-bottomed Dutch oven set over medium heat, and when it foams, add the onions, garlic and parsley. Cook, stirring often, until soft, 5 to 7 minutes. Add the mushrooms, and cook, stirring often, until they are soft and have given up their liquid, 5 to 7 minutes. Add wine or stock, and stir to deglaze the pan, then cook until the liquid has evaporated, 5 minutes.
• Add the ground pork and the spices, and cook until the pork has lost its pinkness, 5 to 7 minutes. Add grated potato, and cook another 5 to 7 minutes. Remove from heat.
• Shred the cooked chicken or turkey into the pot along with the cooked pork and about 1/2 cup of its braising liquid, stir lightly to combine and season to taste with salt and pepper. Chill in the refrigerator for at least an hour and up to a day.
• Assemble the pie. Place a large baking sheet on the middle rack of oven, and heat to 400.
• Remove one disk of dough from the refrigerator, and using a pin, roll it out on a lightly floured surface until it is roughly 10 to 11 inches in diameter. Fit this crust into a 9-inch deep-dish pie plate or cast-iron pan, trimming it to leave an overhang. Place this plate, with the dough, in the freezer.
• Roll out the remaining dough on a lightly floured surface until it is roughly 10 to 11 inches in diameter.
• Remove pie crust from freezer, and put the chilled filling into it. Cover with remaining dough. Press the edges together, trim excess, then crimp the edges. Using a sharp knife, cut three or four steam vents in the top of the crust. Paint the pie's top with the egg wash.
• Place pie in oven on hot baking sheet, and cook for 20 minutes, then reduce temperature to 350, and cook until the crust is golden brown and the filling is bubbling, about 30 to 40 minutes more. Let cool 20 minutes before serving.