Adapted from: Julia Child in New York Times
3 large carrots
2 medium onions
2 ribs celery
2 medium leeks, white and tender green portions
1/2 teas dried tarragon
salt and pepper to taste
3 pound (approximately) chicken, cut up or a mixture of chicken pieces, skin removed if you prefer
1 1/2 c dry white vermouth
1 1/2 to 2 c chicken broth
1/2 c heavy cream
1 1/2 teas cornstarch
6 egg yolks
3 T minced fresh parsley (Italian, preferably)
After cleaning the vegetables, cut them into julienne (or cut them anyway you'd like, keeping them relatively the same size). Cut vegetables should equal about 5 cups in all. Add tarragon and a some salt and pepper and mix, if you have room in your measuring cup.
In a Dutch oven, layer the ingredients, starting with one third of the vegetables, then half the chicken and so on. Salt and pepper the chicken pieces as you place them in the pot. Pour in the vermouth and enough chicken broth to barely cover the ingredients. You can refrigerate the pot at this point and cook several hours later.
When ready to cook, bring the pot to a simmer, covered and cook slowly for 30 minutes or until chicken is tender and has reached temperature of 165F.
Remove chicken from sauce, cover and keep warm while you strain the cooking liquid, reserving vegetables as well. You may remove some of the excess oil from the liquid, if desired.
Whisk the cream and cornstarch in a small bowl until smooth. Whisk the egg yolks in a large bowl and stir in the cream mixture. Very slowly, stir in the hot cooking liquid taking care to keep the eggs from curdling. This may be most easily accomplished using a ladle, since a heavy Dutch oven would be hard to hold with one hand. Return chicken, vegetables, and sauce into the Dutch oven and over medium-low heat, stirring gently from time to time, reheat all but do not bring to a boil.
To serve ladle into large warm soup bowls and sprinkle with parsley. Serve with boiled potatoes or egg noodles or a loaf of crusty bread.
While searching the internet I found recipes using sauvignon blanc rather than the vermouth. I haven't tried it but I imagine it would work just fine.
I prefer to remove the skin from chicken before braising or stewing because I don't see a way to keep the skin crispy and it becomes unpalatable to me.
When I made this, I had just read of a Cook's Illustrated method which increases the flavor of chicken stews and soups. They recommend browning removed skin which creates flavorful "fond" and some fat, (which can be poured out, but hang on to the fond). For a full discussion of the technique, see this from cookscountry.com. Remove the browned skin pieces before layering the ingredients in the pot. I also browned the the back and wings (left over from when I cut up the chicken) and cooked them with the rest of the dish discarding them before combining the vegetables and chicken with the finished sauce. I browned the skin, back, and wings while I prepped the vegetables so it didn't add any extra time.