Cut the chickens into pieces. Heat 3 tablespoons each of oil and butter and cook the pieces without browning. Remove them, keep warm. Place 1 tablespoon butter in the same pan, add the shallots, and carrot and cook for 5 minutes, stirring. Replace the chicken pieces. When hot, flame with the Cognac. Add the white wine, sprigs of tarragon, salt, pepper and a little water to nearly cover the chicken. Cover and bring to a boil, lower the heat and simmer for 30 minutes. Remove the pieces of chicken and place them in a serving dish. Beat the cream with an egg yolk and flour and pour into the sauce. Heat just to boiling and then strain through a sieve over the chicken. Sprinkle with chervil and tarragon.
