Par-cook chickpeas: Drain, cover with fresh water, boil vigorously 10 minutes, then drain.
Roast garlic: Heat oven to 200°C/400°F. Slice off top ¼ inch, drizzle 1 tbsp oil, pinch of salt, wrap in foil on a baking sheet; roast 30–35 minutes. Cool slightly.
Build base: Heat remaining 3 tbsp oil in a Dutch oven over medium. Sauté onion and leek 7–8 minutes until translucent. Add carrots and celery; cook 5 minutes.
Simmer: Add chickpeas and broth. Season with salt, pepper, oregano, and smoked paprika. Bring to a gentle simmer, reduce to low, cover, and cook 60–75 minutes, until chickpeas are very tender and crush easily between fingers.
Emulsify: Squeeze roasted garlic from skins. Blend about 3 cups of the soup with garlic and tahini until completely smooth (vent lid and blend in batches if using a standard blender).
Finish: Stir purée back into pot. Over medium-low, add lemon juice, spinach, dill, and parsley; cook 2–3 minutes until spinach wilts. Adjust seasoning.
Serve: Ladle into bowls; garnish with dill, optional 1 tsp oil per serving, and lemon wedges.