In a large dutch oven, saute the chicken pieces with 2 tablespoons of oil for 5 minutes on high heat, turning the chicken once. Remove from the pan and set aside.
Add the onions to the dutch oven and saute over medium heat for about 15 minutes or until lightly golden.
Add garlic and turmeric and saute for 2 additional minutes.
Add the tomato paste and continue to saute for 2 minutes.
Return the chicken and add tomatoes and water, cover and bring to a gentle boil. Reduce heat and simmer on low heat for 30 minutes.
While the chicken cooks, toss the peeled and quartered eggplants with 1 teaspoon of salt.
In a large frying pan saute the eggplants over medium-low heat adding as much oil as needed to brown the eggplants on all sides. About 15 to 20 minutes. Remove from the pan and set aside.
After the chicken has been cooking for 30 minutes, add salt, Ab Ghooreh and Ghooreh. Stir and continue to cook for 30 minutes.
Arrange the partially cooked eggplants on top of the stew and gently press them down to submerge them into the stew.
Cover and cook over low heat for another 30 minutes. Chicken should be tender and readily falling off the bone.
Remove from heat, adjust for seasoning and allow to sit for 5 minutes before serving.
Gently transfer the stew into a serving dish without disturbing the eggplants too much, so that they maintain their integrity.
Serve the stew with Persian saffron basmati rice.