Brown chicken in oil in a heavy pan, in batches if necessary.
While chicken is browning, tie the herbs and peppercorns in cheesecloth with a long piece of kitchen twine.
Drain chicken and keep warm.
Add butter to the pan with carrots, onions, garlic, and celery, salt and pepper. Saute until slightly soft, about 5 minutes.
Sprinkle four over vegetables and quickly stir to mix with butter, then add the wine, a little bit at a time, so sauce does not clump.
Reduce the wine by half, then add the chicken stock. Then add the cheesecloth wrapped herbs (bouquet garnis), tying the string to the pot handle so it doesn't get lost, and add chicken to pan.
Reduce heat and simmer for 35 minutes or so, until chicken is done and tender.
Whisk together the egg mixture in a small bowl and temper it by adding a small amount of the hot cooking liquid at a time, whisking constantly, so eggs do not curdle.
Remove bouquet garnis from pan and stir in egg mixture and lemon zest, checking seasoning and adjusting with more salt and pepper if needed. Cook just one or two minutes to heat that, then remove from heat.
Saute the onions and mushrooms in butter, seasoning with salt and pepper and cooking for about 8 minutes or until lightly browned. Add the wine to the saute pan and deglaze, stirring up any browned bits, and cooking until wine is reduced by half, a few minutes or so.
Place some of the mushroom/onion mixture into a bowl and place some chicken and sauce on top. garnishing with parsley if desired.
Cook's note: I recommend serving this with dry white wine, fresh baguette with softened herb butter and a tossed salad with freshly made vinaigrette and shaved parmesan (easy accompaniments for a large meal, or cut the recipe down using the serving sizer on the recipe page).