Step 1Remove the little "germ" that is attached to the side of each fava bean. Blanch the beans in plenty of rapidly boiling salted water until tender, 1 to 2 minutes, then transfer them to an ice bath with a slotted spoon to cool. Drain when cool. Blanch the soy beans the same way, 3 to 4 minutes, chill and drain.
Step 2Remove and discard any skins from the soaking beans that have risen to the top of the water. Drain and rinse the marrow beans and cranberry beans and place them in 2 separate pots. Cover each with cold water by at 2 inches and bring to a boil. Remove any bad beans that float to the surface. Drain the beans and run under cold water to cool.
Step 3Return the beans to the pots and cover each with 1/4 cup chicken stock and enough water to cover the beans by three times. Add a slice of leek, carrot and onion to each pot. Heat the liquid slowly and bring to a simmer. Some beans that have not hydrated, and any loose skins will come to the top. Skim them and discard. Simmer the beans until they are tender, 40 to 50 minutes. (The recipe can be prepared up to this point one day ahead and the beans refrigerated in their cooking liquid, tightly covered.)
Step 4Cut the green beans and the yellow wax beans on the bias into pieces that are about 1 inch long.
Step 5When almost ready to serve, drain the cooked marrow and cranberry beans from their liquid and combine with the fava and soy beans in a skillet with about 1/2 of the "Quick" Sauce. Bring to a simmer, skim any impurities and cook until warmed through, about 1 to 2 minutes. Stir in 1 teaspoon of butter, then the green and yellow wax beans, the tomato diamonds, the minced carrot, celery and leek and the salt and pepper to taste. Keep warm while cooking the lamb.
Step 1Loop a piece of kitchen twine around the backside of the bone of a lamb chop. Wrap both ends of the twine around the meat and back to the bone. Tie the twine around the bone to give a uniform shape to the chop. Cut the excess twine and repeat with the remaining chops.
Step 2Wrap the bones in aluminum foil to protect them from burning, season the chops with salt and pepper, and let rest at room temperature for an hour.
Step 3Heat the oven to 375 degrees.
Step 4Heat 1/8 inch of oil in a skillet over medium-high heat. Add the lamb chops and cook for about 3 minutes to brown. Turn the chops and continue to cook for another 3 minutes. Place the chops on their sides and rotate them to brown the sides for another 1 to 2 minutes. The meat should be well browned but still slightly rare.
Step 5Remove the excess fat from the pan (leave the original amount) and add the butter, basting the lamb chops with the butter as it melts. Top the lamb with the garlic cloves and the sprigs of thyme. Place the pan in the oven for about 2 minutes or until the meat is medium rare and a meat thermometer registers 115 to 120 degrees. Remove the pan from the oven and let the meat rest for 3 to 4 minutes.
Step 6Place a portion of the warm bean mixture on each plate. Stand a lamb chop upright on its edge with the bone facing up over the beans. Arrange a few rosemary leaves on the beans and spoon a few drops of basil oil over the beans and the lamb.