Make the stock: Adjust an oven rack to the middle position and heat the oven to 425 degrees. Spray a small flameproof roasting pan with vegetable oil and add the lamb shank. Roast the shank, turning it occasionally with tongs, until it is well browned, about 1 hour. Add the onions, carrots, celery, garlic, and tomato paste and continue to roast, stirring once or twice, until the vegetables have colored, 30 to 45 minutes more. Transfer the contents of the roasting pan to a heavy-bottomed 5- to 6-quart stockpot and set the roasting pan on a burner over high heat. Add the wine and deglaze the pan, stirring with a wooden spoon to scrape up the brown bits. Transfer the deglazing liquid to the pot with the shank and vegetables. Add the thyme, bay, parsley stems, peppercorns, clove, and the water. Bring to a simmer over high heat, then reduce the heat to low and simmer slowly until the stock is rich and flavorful, about 3 hours. Remove from the heat and strain through a fine-mesh conical sieve or chinois into a deep bowl; discard the shank. You should have about 4 cups of stock. Let the stock cool, and then refrigerate it until needed.

Prepare the eggplant and tomatoes for the pilaf: Trim the ends from the eggplants and slice them into ¼-inch rounds. Sprinkle fine sea salt in the bottom of a large shallow glass baking dish or a rimmed baking sheet lined with parchment paper. Arrange the eggplant slices in the dish or pan; sprinkle the tops with salt. Allow the eggplant slices to stand until they release a fair amount of liquid, about 30 minutes. Dry them on paper towels without rinsing and set them aside. Wash and dry the glass baking dish or baking sheet. If using a baking sheet, line it with a fresh parchment sheet.

While the eggplant slices are being salted, prepare the tomatoes. Core the tomatoes and peel them with a sharp paring knife or vegetable peeler. Cut them lengthwise into quarters. Use your fingers to coax the seeds out from the walls of the tomato wedges (fig. 3.1). Discard the seeds. Cut each quarter into 3 pieces and set the tomatoes aside (you should have 2 cups). If you are using canned tomatoes, drain them and use your fingers to remove the seeds. Cut the tomatoes into fairly large pieces and set them aside.

Heat a large well-seasoned cast-iron skillet over medium-high heat. Pour the olive oil into a small bowl. Dip each eggplant slice quickly into the oil and run the slice through your fingers to skim excess oil off the eggplant and back into the bowl. Place them back into the clean baking dish or on the baking sheet. When all the slices have been oiled and the skillet is hot, arrange half of the eggplant in a single layer in the skillet. Lower a large pot lid that fits into the skillet onto the slices to weigh them down (fig. 4.1) and sear, without turning, until the slices are softened and spotty brown, about 40 seconds (fig. 4.2). Lift the lid and peek under the slices to get a sense of how they’re browning). Turn the slices with tongs and sear them on the other side, again using the pot lid as a weight. Transfer the seared eggplant back to the baking dish or baking sheet and cook the remaining slices in the same fashion. When the eggplant is cool enough to handle, stack the slices on top of each other and cut them into quarters. Set aside.

Reduce the lamb stock: Using a spoon or skimmer, remove and discard the congealed fat from the surface of the chilled lamb stock. Pour the stock into a medium heavy-bottomed saucepan and reduce it over high heat until you have just over 2 cups. (If using chicken broth, bring just over 2 cups to a simmer in a saucepan.) Cover the pan, reduce the heat to low, and keep the stock at a bare simmer until needed. 

Make the pilaf: Combine the turmeric, allspice, red pepper flakes, black pepper, cinnamon, and cardamom in a small bowl and stir to combine. Separate the ground lamb into 1-inch bits and place them in a 6- to 8-quart Dutch oven over medium heat. Brown the lamb slowly, turning the pieces only when the bottoms are well browned, 5 to 7 minutes in all; sprinkle the lamb with salt and half of the spice mixture after the bottom pieces brown. When the lamb is done (fig. 6.1), transfer it to a medium bowl. Pour or spoon off all but 2 tablespoons of fat from the Dutch oven. Add the onions to the pot, sprinkle them with salt and the remaining spice mixture, and cook over medium heat, stirring frequently, until softened and browned, 5 to 7 minutes (fig. 6.2). Stir the rice into the onions and sauté, stirring constantly, until the rice is opaque and separated into individual grains, about 2 minutes (fig. 6.3). Add the browned lamb, the tomatoes, the eggplant, the simmering stock, and ½ teaspoon salt and stir to combine. Bring to a simmer over medium heat, then reduce the heat to low. Cover the Dutch oven and cook for 20 minutes. After 20 minutes, check to see if the rice has swollen and if most of the liquid has been absorbed. If that is the case, remove the pot from the heat and allow the pilaf to rest, covered, for 5 minutes. If the rice is still firm and the dish wet, cover the pot and continue to cook for 10 minutes more, and then allow the pilaf to rest for 5 minutes. Stir in the chopped parsley and taste for seasoning. Serve very hot with a big spoonful of yogurt on each portion.