This recipe makes a fine sauce, the amount of flour in it makes the filling slightly poolish, if you really desire a tight sauce, add up to 1/4 cup more flour. I am currently developing a two crusted pie, but this works.
Make the pastry: Stir together the flour, and salt, and sugar, if using. Add the shortening and cut inches Stir in the water, and make a paste, adding a few more drops if nessecary to form a cohesive dough. Gather in plastic wrap, tightening, and forming into a loose rectangular shape, then allow to chill.
Poach the chicken, follow the rules carefully, lest they burn.
Wash to clean the chicken, removing any innards, set aside for another use. Tie the legs together with string. Put the chicken into a spaghetti pot, adding the prepared broth, the vegetables, the seasonings, including all the salt, and enough waster to almost cover the chicken.
Bring to a furious boil, then turn down the heat to low or medium low, however it will simmer delicately, and cook for about 40 minutes, the leg joint should just wiggle a little bit, but the hen should not nessecarily be done. Turn off the heat, transfer the stockpot to a side of the kitchen, lid half ajar, and let the chicken cool gently, for at least an hour, while other things get done, do not remove the chicken from the broth, until ready to proceed.
Make the sauce: Working over medium heat, put the bacon slices, and 1 tablespoon oil into a 12-inch sauté pan. Cook and stir the bacon until it is done, there should not be any fat left, it should look crisp. Remove to a plate, leave fat in pan, and deglaze the mixture with one or two tablespoons of water.
Add the sliced green onions, the shallots, and a pinch of salt. Cook gently, until tender but not brown, it is okay to get the s little brown, if you want, but unnecessary.
Measure and stir in the flour, cook the roux gently, adding more of the reserved oil, if nessecary to make a smooth paste, it will not require a lot, but it will probably require some. Turn the heat down to low, or remove the pan from heat.
With a carving fork, or tong, remove the chicken to a plate, and set aside. Gather a 1-cup measure, and a small, fine sieve, and also a whip.
Return pan to heat, increase heat. Add 5 cups of the broth through the strainer. Work in batches if it feels necessary, I usually add all of the broth, before whisking and brining to the boil, whisking all the time, but if you have fear, of these types of sauces, one or two cups, at the time can be added. Remove the mixture from the heat and set aside, salt can be added later.
Detach the legs (thighs) from the body of the chicken. I like two peel the chicken in the stages, it's neater, and makes less likely, that anything stray will suffer the pot. First, pull all of the skin from the chicken and discard, detaching the wings (with a steak knife, if nessecary), from the breasts, and pulling off any pieces of gristle or bone, take off all of the rib pieces too, and throw all of that away, or transfer to a separate pile.
Pull the breasts from the body, find the tender, and detach it, taking away the thin white membrane that surrounds it. Chop off the piece of connective gristle that hangs from the top of the breast, sometimes, also, I tear off the very hard, tip end, to make way for smoother meat. Set the breast aside, discarding any refuse.
Pull off all of the thigh meat in batches, discarding all of the pieces of lumpy fat, that surround the different lobes. The leg meat will be very tender and flavorful, and I often leave it in bigger pieces, but chop as desired.
Chop the tenders, then slice the breast into two, slice the larger half into three, and chop, the smaller, into two, and chop likewise.
Put all of the meat into the pot of sauce, stirring. The breast and thigh meat provides more than enough protein to fill the prepared dish, and I rarely pick the meat from the drumsticks or wings, just chill the and use for a mayonnaise sandwich, use them if you wish.
Add the frozen peas, to the pot, stir, set aside.
Put the pot of broth back onto the stove, trim ends from the carrots and celery, do not slice then. Put into the broth and bring to the boil. Simmer until each is done. They cook at different rates, the carrots will require ten to fifteen minutes cooking, and should be soft, they do not need to be al dente, it will do them detriment.
Remove to a plate, slice and put into the sauce. Continue cooking the celery another five minutes. Remove, slice fine, add to sauce.
Taste the sauce for salt and pepper, it may only need a little. Stir in the reserved, crumbled bacon.
Transfer to a clean dish of 9x13 inch capacity. The dish does not necessarily need to be greased. Smooth the top, set aside while the paste gets rolled.
It is a good idea to use a rule when rolling the paste, because I find that persons always overestimate and end up with too much overhang, but eyeball it if you wish.
Flour a surface, place on the pastry, flour it well, and a rolling pin, keep in a rectangle, and roll to fit the dish.
Trim any overhang by an inch, then gather up the excess and make a glut on the rim.
Mix together the egg yolk, cream and a little pinch of salt. Pant the top of the pastry, eliminating any egg that pools in the crevice, slash three holes in the top, with a scalpel or sharp knife.
Put into a preheated 425 degree oven and bake till golden, about 40 minutes, check after 30, till done.
Rest 5 minutes before serving. It is best served by cutting a serving of pastry, removing it to one side, spooning out the filling, with a large server, and then shuffling the paste over to the top of the pie serving. Serve hot, leftovers are good at room temperature. Reheats nicely. Enjoy.