Cook the chicken and make the stock: Combine the chicken neck (if using), the onions, carrots, celery, garlic, thyme, bay leaf, parsley stems, and water in a heavy-bottomed, 5- to 6-quart stockpot. Place the chicken breast up in the pot and bring the liquid to a simmer over medium-high heat. Reduce the heat to low, cover the pot, and simmer gently until the chicken legs pull easily from the carcass, about 1 hour. Remove from the heat and let cool at room temperature for 20 minutes.

Using tongs, transfer the chicken from the pot to a rimmed baking sheet. When it is cool enough to handle, pull the meat from the bones and chop it into pieces that fit on a spoon. You should have about 1¼ pounds of meat, or slightly more. Season the chicken with salt and pepper while it is still warm. Cover and refrigerate. Return the bones to the stockpot, bring the stock to a simmer over medium heat, and simmer gently until it is rich, flavorful, and reduced to a generous 7 cups—about 1 hour. Strain the stock through a fine-holed colander or chinois into a large mixing bowl. Let it cool, cover, and then refrigerate overnight.

Reduce the stock: Lift the congealed fat—or schmaltz—from the top of the stock with a spoon; some stock will cling to the schmaltz, but this is fine. There will be anywhere from 6 to 10 tablespoons of schmaltz, depending on the chicken. Set it aside. Pour the stock into a medium saucepan and bring it to a simmer over medium-high heat. Simmer for about 15 minutes, until 6 cups of stock remain. Remove from the heat and cover to keep hot.

Make the filling: Adjust an oven rack to the middle position, set a roasting pan on the rack, and heat the oven to 475 degrees. Toss together the parsnips and carrots in a mixing bowl. Melt ½ cup of the schmaltz (if you do not have ½ cup of schmaltz, make up the difference with butter) over low heat in a Dutch oven, and then remove the pot from the heat. Spoon 1½ tablespoons of the melted fat onto the vegetables, sprinkle them with ¼ teaspoon salt and several grinds of pepper, and toss to combine. Roast the vegetables, tossing occasionally, until they are just softened and have begun to color, 15 to 20 minutes, depending on their size. While they are roasting, toss the mushrooms in a bowl with 1½ tablespoons schmaltz, ¼ teaspoon salt, and several grinds of pepper. When the parsnips and carrots are done, transfer them to a mixing bowl, and then turn the mushrooms into the roasting pan. Roast the mushrooms, tossing occasionally, until they lose their juices and begin to color, about 10 minutes. Transfer the mushrooms to the bowl with the parsnips and carrots.

There should be 4 to 5 tablespoons of schmaltz remaining in the Dutch oven. Add the leeks to the Dutch oven and cook, covered, over low heat, stirring occasionally, until the leeks are softened, about 5 minutes. Transfer the leeks to a bowl with a slotted spoon, leaving the schmaltz in the Dutch oven. Stir the flour into the pot with a wooden spoon; if there is not enough fat to coat the flour and form a nice roux, add an additional tablespoon or so of schmaltz or butter. Cook, stirring, until the flour is golden, about 3 minutes. Add a ladle of hot chicken stock to the roux and whisk vigorously. It will thicken quickly. Add the remaining hot stock, whisking constantly to prevent lumps. Stir in the vermouth. Season with 1 to 1¼ teaspoons salt and at least ½ teaspoon pepper and simmer gently for 5 minutes. Return the leeks to the pot, and then add the reserved chicken meat, the roasted vegetables, and the thyme. Taste for seasoning. Set the filling aside or let it cool, cover, and refrigerate overnight.

Roll out the pastry bottoms and line the pans: Clear some space in your refrigerator and set a rimmed baking sheet on a shelf. Grease eight 4¼-inch pie pans with a 1-inch depth or similarly sized molds with the softened butter and set them aside.

Remove the dough from the refrigerator and whack it sharply with a rolling pin to flatten it slightly. Cut the dough in half and return one half to the refrigerator. Roll out the other half on a lightly floured work surface into a 12-inch square, taking care to roll evenly from the center to the edges of the dough. With a 6-inch round cutter, stamp out 4 rounds of dough (fig. 7.1) and fit them snugly into the greased pans (fig. 7.2). If the dough balloons out, prick it with a toothpick or wooden skewer. Work quickly so the dough does not become warm. Set the dough-lined pans on the baking sheet in the refrigerator. Gather up the dough, lightly flour the work surface, and roll out the dough. Stamp out 3 more rounds and fit them into 3 pans. Roll out the last bit of dough, stamp out a final round, and line the last pan. Set them in the refrigerator with the first four.

Roll out the pastry tops: Remove the second piece of dough from the refrigerator and repeat the process described in Step 7 to roll and stamp out the eight 6-inch rounds that will become the top crusts of the pot pies. Stack the rounds between pieces of parchment or plastic wrap and refrigerate them.

Blind bake the bottoms: Adjust the oven racks to the lower- and upper-middle positions and heat the oven to 400 degrees. Line each chilled dough-lined pan with a 6-inch square of aluminum foil and fill with about 1 cup of dried beans (fig. 9.1). Arrange 4 pans on each of 2 baking sheets. Bake for 15 minutes, rotating the baking sheets front to back and top to bottom halfway through. Remove the baking sheets from the oven and gently lift out the aluminum foil and beans (fig. 9.2). Position an oven rack in the middle of the oven. Leave the oven on.

While the bottom crusts are baking, return the filling to the stove and heat it over low heat until warmed through.

Fill and bake the pies: Beat the egg and water in a small bowl, and then pour the mixture through a tea strainer into a second small bowl. Fill each of 4 still-warm bottom crusts with 1 cup of filling and brush the edges of the dough with egg wash (fig. 11.1). Place a round of dough over the top of each pie and roll the edges under slightly to meet the edges of the bottom crust (fig. 11.2). Crimp the edge (fig. 11.3). Brush the top crusts with egg wash and, using kitchen shears, snip a vent into the top of each pie (fig. 11.4). Arrange the 4 filled pies on a rimmed baking sheet. Return the unfilled bottom crusts to the oven for 30 seconds to warm them. Bake the filled pies until the tops are golden brown and the filling is hot, about 15 minutes. While the first 4 pies are baking, fill and top the remaining 4 pies. When the first 4 pies are finished, remove them from the oven and bake the second set of pies. Let the baked pies cool in their pans for 10 minutes, then gently lift the pot pies from the pans and set them in individual serving bowls. The first set of pies may be rewarmed briefly after the second set comes out of the oven, or they may all be baked in advance and rewarmed.