Prepare the piecrusts as described. Divide the dough into 4 parts and form into 4 disks. Wrap each disk in plastic wrap and refrigerate for at least 30 minutes before rolling 2 disks out to fit into two 9-inch deep-dish pie pans. Trim the edges of the dough so that 1/2 inch hangs over the sides of the pans. Roll the remaining 2 disks out and refrigerate (placed on a baking sheet with plastic or parchment between the crusts), along with the fitted piecrusts, until you are ready to bake the potpies.
Season the chicken pieces with the salt and black pepper. Heat a Dutch oven or other large heavy pot over high heat and brown the chicken pieces on both sides in the olive oil, working in batches if necessary, about 5 minutes on each side. Drain all the fat from the Dutch oven and add the chicken Stock, bay leaf, poultry seasoning, and Chicken Rub. Bring to a boil, cover, reduce the heat to low, and simmer until the chicken is very tender and falling from the bone, about 1 hour. Using a slotted spoon, transfer the chicken pieces to a plate and set aside until cool enough to handle. When the chicken is cool enough to handle, remove the meat from the bones and tear into bite-size pieces. Set aside.
Meanwhile, add the potato, carrots, onions, corn, mushrooms, lima beans, and heavy cream to the Dutch oven and return to a boil. Cover the pot, reduce the heat to a simmer, and cook until the vegetables are very tender, about 30 minutes.
Combine the flour and butter in a small bowl to form a thick paste. Ladle some of the hot chicken broth into the bowl and whisk to combine with the flour-butter paste. When smooth, add to the pot and stir to combine well. Bring the sauce to a low boil and continue to cook until the sauce is thick and smooth, about 5 minutes. Add the reserved chicken meat, stir to combine, and remove from the heat. Discard the bay leaf, taste and adjust the seasoning if necessary. Set aside to cool completely. Once cooled, refrigerate until thoroughly chilled.
Preheat the oven to 400?F and position an oven rack on the lowest rung of the oven.
Divide the chilled filling between the two chilled pastry-lined pie pans and, using a spatula, smooth the filling to the edges. Place the egg in a small bowl and beat with 1 tablespoon of water. Lightly brush the edges of the overhanging pastry with some of the egg wash. Top each potpie with a rolled-out crust and trim the edges to match those of the bottom crusts. Using your fingers, pinch the edges of dough together and roll inward so they sit inside the edges of the pie pans; decoratively crimp. Using the tip of a sharp knife, cut several decorative slits in the top of each pie to allow steam to escape while cooking. Brush the top of each potpie with some of the egg wash.
Bake the potpies for 20 minutes. Reduce the oven temperature to 350?F and continue baking the potpies until the crusts are golden brown and the filling is heated through, about 40 minutes longer.
Remove the potpies from the oven and allow to cool slightly before serving. Cut the potpies into wedges and serve.
Makes two 9-inch deep-dish potpies, 12 servings