Marinade: Dice the carrots, celery, and onion.
Coarsely chop the thyme, bay leaves, rosemary, parsley, and garlic.
Add salad oil and mix all of the ingredients together in a large bowl.
Rub the mixture over the rack of lamb and marinate for 48 hours, turning occasionally.
Lamb: Remove the lamb from the marinade and drain.
Strain the vegetables in the marinade and reserve.
In a large roasting pan, brown the lamb bones at 500 degrees F for 15 minutes.
Add drained mirepoix (the strained vegetables) from the marinade and brown another five minutes.
Strain the contents of the roasting pan to eliminate fat and then transfer the bones and vegetables to a stock pot.
Add 6 chopped mushrooms and mint, then deglaze the roasting pan with red wine and add the liquids to the stockpot.
Add the demi-glace and bouquet garni and cook for two hours, skimming carefully and adjusting seasoning.
Strain this sauce through chinois into a pan.
Heat the sauce.
Add julienned ham, pickle, and 2 mushroom tops to sauce and adjust seasoning.
Salt and pepper racks of lamb and sprinkle with thyme.
Put racks of lamb in a roasting pan and roast for 15-18 minutes.
Remove rack from roasting pan and let racks rest for five minutes before carving.
Blanch carrots and snow peas, then sauté in butter and reserve.
(Season snow peas with salt, sugar, and black pepper.)
Cut racks in half, four ribs per person.
Warm sauce and ladle around racks.
Garnish with sautéed carrots, snow peas, and watercress.
