The day before serving the dish, season the lamb racks with salt and pepper, cover, and refrigerate until needed, then make the stock.
To make the stock: Preheat the oven to 375 F. Place the lamb bones and trimmings in a large shallow roasting pan and bake in the preheated oven, turning them occasionally, for 30 minutes, or until evenly browned. Transfer the bones and trimmings to a large stockpot, reserving the roasting pan. Add the water to the stockpot and bring to a boil over high heat. Reduce heat to a simmer and skim the scum that rises to the surface for the first 10 to 15 minutes. Simmer for 3 hours, uncovered.
While the bones are simmering, place the roasting pan over medium-high heat and add the onion, carrot, celery, and tomato paste. Cook the vegetables, stirring occasionally, until they are golden and caramelized, about 8 to 10 minutes. When the vegetables are browned, add the wine to the pan and cook, stirring to scrape up the browned bits from the bottom of the pan; set aside. When the bones have simmered for 3 hours, add the browned vegetables and the remaining stock ingredients to the stockpot. Pour the remaining 3 quarts of water to cover into the stockpot and continue to simmer for 3 hours more hours, monitoring to be sure the moisture does not completely evaporate. Remove the stock from the heat and strain through a fine-meshed sieve. Chill well, then discard the layer of fat that has congealed on the top.
To make the lamb sauce: Heat the olive oil in a deep, heavy pot and saute the lamb scraps until brown, about 7 to 9 minutes. Add the carrot, onion, and celery and cook until golden, about 5 to 7 minutes. When the vegetables are cooked, add the Burgundy and stir to scrape up the browned bits from the bottom of the pan. Add the lamb stock, thyme, and rosemary. Simmer uncovered until reduced by half, about 1-1/2 to 2 hours. Add salt and pepper, strain, cover, and refrigerate.
The next day, make the persimmon chutney: Puree all the chutney ingredients in a blender or food processor until smooth, about 30 seconds. Strain through a fine-meshed sieve and set aside.
To make the peanut crust: Combine all the ingredients and set aside.
Preheat the oven to 400 F. Combine all the ingredients for the marinade in a shallow pan and mix well. Add the lamb racks, coating them well with the marinade, and marinate at room temperature for 10 to 15 minutes. Remove the racks of lamb from the marinade and sear them on a grill over hot coals, or in a heavy saute pan or skillet, for 2 minutes on the first side, then 1 minute on the other side. Take the lamb from the grill or pan and coat both racks with the persimmon chutney mixture. Dust the chutney coating with the peanut crust and transfer to a shallow roasting pan.
Roast the lamb in the preheated oven for 18 minutes for rare, 22 minutes for medium-rare, and 28 to 30 minutes for medium. While the lamb is cooking, reheat the sauce in a small saucepan and adjust the seasoning.
To serve: Slice the lamb racks into eight 2-bone portions. Serve two 2-bone portions on a pool of lamb sauce for each diner. Chef Williams accompanies the lamb with roasted baby vegetables and rice pilaf.