Slice eggplant lengthwise into 1/2 -inch-wide slices, then crosswise into 1-inch-wide pieces; set aside. Rub lamb shanks with 1 tablespoon sumac, salt and pepper.
Heat 1 tablespoon oil in a large Dutch oven (or other 5- to 6-quart pot) over medium-high heat. Add the lamb; cook, turning often, until browned on all sides, 5 to 7 minutes total. (Don’t overcrowd the pan; brown in batches if necessary.) Transfer to a plate.
Add the remaining 1 tablespoon oil to the pot; add bell pepper, onion, 2 minced garlic cloves and the remaining 1 tablespoon sumac. Cook, stirring often, until the vegetables are beginning to soften, 3 to 5 minutes. Return the lamb to the pot. Stir in the eggplant, tomatoes and water. Bring to a boil. Reduce heat to maintain a simmer, cover and cook, stirring occasionally and turning the shanks over once about halfway through, until the lamb is very tender, about 2 hours.
Remove the lamb to a plate and tent with foil to keep warm. Increase heat to medium-high and cook the sauce until slightly reduced and thickened, 5 to 10 minutes. Remove from heat and stir in 1/4 cup parsley.
Combine the remaining 1/4 cup parsley and the remaining garlic in a small bowl. Serve the lamb and vegetable sauce topped with the parsley-garlic mixture.
NOTE: If you’re using large, common globe eggplant, which can be more bitter than other varieties, salting beforehand can reduce bitterness. To salt: Place prepped eggplant in a large colander over a bowl and mix with 1 tablespoon salt. Top the eggplant with a plate weighted down with cans. Let sit for 30 minutes to 1 hour before using. Rinse well with cold water, then dry with paper towels.