In a large heavy skillet, warm up 2 tablespoons of oil, and brown the chicken on all sides over medium-high heat. Leaving the chicken in the skillet, lower the heat and add the shallots, cinnamon sticks, cardamom and chicken stock. Season with salt and pepper to taste. Bring to a boil on high heat. Cover, lower the heat to medium, and simmer for another 30 to 35 minutes.

Remove the chicken from the skillet and reserve the stock. When cool enough to handle, remove the skin and bones and discard.

Add 4 tablespoons of oil to a large frying pan and cook the eggplant 5 minutes on each side. Remove and pat dry on paper towels.

Mix the turmeric with 1⁄2 cup of the reserved stock. In the skillet, warm the remaining 2 tablespoons of oil over medium-high heat, add the rice, and cook until it becomes translucent, about 10 minutes. Remove half of the rice and reserve. Flatten the remaining rice in the skillet and layer 1⁄2 the eggplant and all the chicken pieces. Cover with the remaining eggplant and top with the remaining rice. Pour the turmeric-stock mixture over the rice and add 5 cups of the reserved stock. Cover the skillet. Bring to a boil, lower the heat to medium, and cook for about 30 to 35 minutes, or until all the liquid is absorbed. Allow to rest 10 minutes.

To serve, use a platter, like a tatin tart, and unmold the chicken tatin on the platter. Add the pine nuts, raisins and a bowl of yogurt as an accompaniment.