Cook the beef in a pressure cooker or heavy pot with water until very tender, about 1 to 1 1⁄4 hours in a pot or 40–60 minutes in a pressure cooker. Shred and drain the meat, season with cumin, harissa, cilantro (if using), salt, and pepper, and cool slightly.
Soak the artichoke halves in lemon water while you work to prevent discoloration. Scoop each half into a small boat, keeping pairs together, and pat dry.
Stuff each artichoke boat with the shredded beef, pressing to fill. Dredge in flour, shake off excess, dip in beaten egg, and shallow-fry in batches until lightly golden. Drain on paper or a rack.
In a wide, ovenproof sauté pan, warm olive oil over medium heat. Add chiles and garlic and cook until fragrant, about 1 minute. Add crushed red pepper, sugar, turmeric, cumin, preserved lemon, coriander seeds, and stir to bloom the spices for 30 seconds.
Add the diced Jerusalem artichokes and leeks; sweat over low heat until softened and beginning to color, about 6–8 minutes. Pour in the water, bring to a gentle simmer, and nestle the fried stuffed artichokes into the sauce. Drizzle with a little olive oil, cover, and simmer gently until artichokes are tender, about 35–45 minutes.
Transfer, covered, to an oven preheated to 350°F/180°C for 20 minutes to finish cooking and concentrate flavors. Uncover, increase oven to 400°F/200°C, and roast 8–12 minutes until browned and sauce is reduced to a glossy, spoonable consistency. If the sauce is too thin, return to the stove and reduce; if too thick, add a splash of water. Finish with a drizzle of olive oil before serving.