In a large dutch oven, saute the lamb shank with 2 tablespoons of oil for 5 minutes on medium-high heat, turning a few times. Remove from the pan and set aside.
Add the onions to the dutch oven and saute over medium heat for about 10 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 lamb, add tomatoes and water, cover and bring to a gentle boil. Reduce heat and simmer on low heat for 60 minutes.
While the lamb cooks, toss the peeled and quartered eggplants with 1 teaspoon of salt.
In a large frying pan, saute the eggplants over medium-low heat with oil to lightly brown the eggplants on all sides, about 15 to 20 minutes. Remove from the pan and set aside.
After the lamb has been cooking for 60 minutes, add salt, pepper, verjuice, 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. Lamb should be tender at this stage.
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.