Remove the rind and cut the bacon into lardons (rectangles 1/4-inch across and 1-inch long). Simmer for 10 minutes in 2 quarts of water. Rinse in cold water. Dry.
In a heavy large heavy bottomed casserole or Dutch oven, saute the bacon slowly in hot butter until it is very lightly browned (temperature of 260 degrees F for an electric skillet). Remove to a side dish.
Dry the chicken thoroughly. Brown it in the hot fat in the casserole. (360 degrees F for the electric skillet.)
Season the chicken with salt and pepper. Return the bacon to the casserole with the chicken. Cover and cook slowly (300 degrees F) for 10 minutes, turning the chicken once.
Uncover, and pour in the cognac. Averting your face, ignite the cognac with a lighted match. Shake the casserole back and forth for several seconds until the flames subside.
Pour the wine into the casserole. Add just enough stock or bouillon to cover the chicken. Stir in the tomato paste, garlic and herbs. Bring to a simmer. Cover and simmer slowly for 20 to 25 minutes, or until the chicken is tender and its juices run a clear yellow when the meat is pricked with a fork. Remove the chicken to a side dish.
While the chicken is cooking, prepare the onions and mushrooms.
Simmer the chicken cooking liquid in the casserole for 1 to 2 minutes, skimming off fat. Then raise the heat and boil rapidly, reducing the liquid to about 2 1/4 cups. Correct seasoning. Remove from heat, and discard bay leaf.
Blend the butter and flour together into a smooth paste (beurre manie). Beat the paste into the hot liquid with a wire whip. Bring to the simmer, stirring and simmer for 1 to 2 minutes. The sauce should be thick enough to coat a spoon lightly.
Arrange the chicken in a casserole, place the mushrooms and onions around it and baste with the sauce. If the dish is not to be served immediately, film the top of the sauce with stock or dot with small pieces of butter. Set aside uncovered for no longer than 1 hour or cool, cover and refrigerate until needed.
Shortly before serving, bring the casserole to a simmer, basting the chicken with the sauce. Cover and simmer slowly for 4 to 5 minutes, until the chicken is heated through.
Serve from the casserole, or arrange on a hot platter. Decorate with sprigs of parsley.
When the butter and oil are bubbling in the skillet, add the onions and saute over moderate heat for 10 minutes, rolling the onions about so they will brown as evenly as possible. Be careful not to break their skins. You cannot expect to brown them uniformly.
Braise them as follows: Pour in the stock, season to taste, and add the herb bouquet. Cover and simmer slowly for 15 to 20 minutes until the onions are perfectly tender but retain their shape, and the liquid has evaporated. Remove herb bouquet. Serve them as they are.
Bake them as follows: Transfer the onions and their sauteing fat to a shallow baking dish or casserole just large enough to hold them in 1 layer. Set uncovered in upper third of a preheated 350 degree F oven for 40 to 50 minutes, turning them over once or twice. They should be very tender, retain their shape and be a nice golden brown. Remove herb bouquet. Serve them as they are.
Place the skillet over high heat with the butter and oil. As soon as you see that the butter foam has begun to subside, indicating it is hot enough, add the mushrooms. Toss and shake the pan for 4 to 5 minutes. During their saute the mushrooms will at first absorb the fat. In 2 to 3 minutes the fat will reappear on their surface, and the mushrooms will begin to brown. As soon as they have browned lightly, remove from heat.
Toss the shallots or green onions, if using, with the mushrooms. Saute over moderate heat for 2 minutes. Sauteed mushrooms may be cooked in advance, set aside, then reheated when needed. Season to taste just before serving.