Wipe the chicken inside and out with a cloth wrung out in boiling water. Cut into 10 serving pieces: 2 drumsticks, 2 thighs, 2 wings and 2 breasts halved. Scrape the carrots and peel the onions. Wipe the mushrooms with a damp cloth and trim the stalks.
Melt the butter in a heavy iron cocotte [heavy frying pan or Dutch oven] over low heat and when foaming add the pieces of chicken, the carrots and onions, and the herbs tied together. Season with salt and pepper, add the wine, cover and cook for 30 minutes, moving the ingredients around occasionally to prevent colouring.
When the carrots and onions are tender remove them with a slotted spoon, cover and keep hot over a pan of boiling water.
Slice the mushrooms finely, add to the pan, sprinkle with salt, cover and simmer for a further 20 minutes. Beat the egg yolks into the cream and set aside.
Remove the chicken from the pan to a heated serving dish, place the vegetables around it in small groups, cover with foil and keep hot.
Using the back of a fork, work the meat residue from the bottom of the pan into the cooking juices. Bring to boiling point, remove the herbs, and draw the pan from the heat. Add a tablespoon of pan juices to the cream, stir well and return this mixture to the pan, stirring constantly until thick.
Pour immediately over the chicken and serve without delay.
Serves 6.