Place chicken in bowl, sprinkle with fines herbs, salt, pepper and garlic. Add chopped onion, carrot, ham, bay leaf. Pour over wine. Refrigerate covered, turning once or twice, 8 hours or overnight.

Soak top and bottom of 3 1/4 quart (3.25 l) clay cooker in cold water about 15 minutes and drain.

Place chicken, vegetables, marinade in cooker. Saute mushrooms in 2 Tb butter until light brown; add to chicken. Warm brandy slightly; ignite and pour flaming over chicken. Place covered cooker in cold oven. Set oven at 450F/230 °C. Bake, stirring once or twice, until chicken is tender and brown, about 1 1/4 to 1 1/2 hours. Pour off cooking liquid; skim and discard fat. Turn off oven, return uncovered cooker to oven. Transfer cooking liquid to large skillet; mix remaining butter with flour until smooth and stir into cooking liquid. Heat to boil and cook, stirring constantly, until thickened and clear, 5-8 minutes. Pour sauce over chicken, garnish with parsley.