Cut the Lamb Shoulder into bite-sized pieces, season with Salt and Black Pepper, then heat Olive Oil in a heavy pot and brown the lamb in batches until well caramelized; remove and set aside.
In the same pot add a little more oil if needed, then sauté chopped Onion until soft and translucent; add minced Garlic and cook for about 30 seconds until fragrant.
Stir in the Tomato Paste and cook briefly to deepen its flavor, then add chopped Tomatoes and cook until they begin to break down and form a sauce.
Return the browned lamb to the pot, pour in enough Water to partially cover the mixture (about 1–2 cups), bring to a simmer, cover and cook for 20–30 minutes until the meat begins to tenderize.
Add the chunked Potatoes and sliced Carrot, stir them in, cover and simmer for about 10 minutes to give these denser vegetables a head start.
Add the Green Beans, sliced Green Bell Peppers and sliced Zucchini; stir gently, recover and simmer another 10 minutes so the vegetables soften but keep some texture.
Fold in the cubed Eggplant (if you salted and drained it beforehand, pat it dry), season with Red Pepper Flakes and taste for seasoning, adjusting with more salt and pepper as needed; simmer uncovered for 15–20 minutes until all vegetables are tender and flavors meld (add a splash more Water if the sauce reduces too much).
Finish by scattering chopped Flat-Leaf Parsley over the stew and drizzling a little extra olive oil if desired; serve hot with bread or rice.
