Wash the chicken, dab dry and cut into 8 pieces. Clean, wash and roughly cut the leek. Peel, wash and roughly chop the carrot. Peel onion and lard with cloves and laurel.
Wash the thyme. Put the chicken pieces, leek, carrot, onion, half of the thyme and peppercorns in a large pot. Cover everything with water (approx. 1 1/2 litres) and bring to the boil. Add 1 teaspoon of salt and simmer for about 40 minutes.
Skim off any foam several times. Clean, wash and slice the mushrooms. Remove chicken parts from the broth. Sieve the broth, measuring a good 1/4 litre (use the remaining broth for other purposes).
Heat 30 g butter in a large pan. Fry the chicken parts in it until golden brown all around. Add the mushrooms and fry for 10-15 minutes more. Chop the rest of the thyme. Heat 30 g butter in a saucepan.
Sweat flour in it. Deglaze with 1/4 liter broth and champagne, bring to the boil. Add thyme. Let everything simmer for about 5 minutes. Stir cream and egg yolk until smooth. Remove sauce from the stove. Stir in the egg yolks (do not boil any more!).
Season the sauce with salt and pepper. Arrange meat and mushrooms on a plate. Add the sauce and serve immediately. Drink: cool champagne.