In a large pot or Dutch oven, heat olive oil over medium-high. Brown the lamb shoulder on all sides. Remove and set aside.
Add onions to the pot and cook until softened. Add garlic, carrots, chickpeas, and spices. Stir for 2–3 minutes.
Return the lamb to the pot and pour in water to cover. Bring to a simmer, then reduce heat to low and cover. Let it cook for 2½–3 hours, until the lamb is fall-apart tender.
Tear flatbread into a serving dish or bowl. Spoon the hot stew directly on top.
Garnish with parsley. Serve hot and share.