Step 1

Toasted Cauliflower Crumbs: Coarsely chop cauliflower and pulse in a food processor until about the size of grains of rice (or, you can very finely chop with a knife instead). You should have about 2 cups.

Step 2

Heat oil in a large skillet, preferably cast iron, over medium-high. Cook cauliflower, stirring often, until golden brown all over and charred in spots, 6–8 minutes. Remove from heat; season with salt and pepper. Let cool in skillet.

Step 3

Lemony Mint Yogurt: Mix yogurt, mint, and lemon juice in a medium bowl; season with salt and pepper.

Step 4

Do Ahead: Yogurt can be made 1 day ahead. Cover and chill.

Step 5

Stew and Assembly: Season lamb shanks very generously all over with salt and pepper. Heat oil in a large Dutch oven or other heavy pot over medium-high. Working in 2 batches, cook lamb shanks in a single layer, turning occasionally, until browned all over, 8–12 minutes per batch. As the shanks finish cooking, transfer to a large plate.

Step 6

Reduce heat to medium; add onions and garlic, cut side down, to the same pot and cook, tossing onions occasionally, until onions are browned in spots and garlic is golden brown, about 5 minutes. Add cinnamon and crushed coriander and cook, stirring constantly, until spices are very fragrant, about 1 minute. Add harissa paste and cook, stirring often and scraping bottom of pot, until vegetables are coated and paste is slightly darkened in color, about 2 minutes. Add 7 cups water, stirring to release any bits stuck on bottom of pot. Season generously with salt and pepper and bring to a simmer. Return lamb shanks to pot and bring stew back up to a simmer. Cover with a lid, leaving slightly askew so steam can escape, and cook, adjusting heat to maintain a very gentle simmer and skimming foam from surface as needed, until meat is tender and easily pulls away from bones, 1½–2 hours.

Step 7

Transfer lamb shanks to a cutting board and let cool 10–15 minutes; keep liquid at a simmer. Pull meat from bones and tear into bite-size pieces. Add bones back to pot as you go. Transfer meat to a medium bowl and cover with plastic wrap.

Step 8

Simmer bones in broth, uncovered, until liquid is thick and very flavorful, 25–30 minutes. Remove from heat; add meat back to pot and let cool uncovered (bones and all) until no longer steaming. Cover pot and chill stew at least 12 hours (you can skip this step, but it will dramatically improve the flavor).

Step 9

Uncover stew and spoon off half to three-quarters of fat on the surface; discard. Gently reheat stew until barely simmering. Pluck out and discard bones and garlic heads (don't worry about any cloves that may have escaped into stew). Taste and season with more salt and pepper if needed. Ladle into bowls and serve with Toasted Cauliflower Crumbs, Mint Yogurt, harissa, and olives, mint leaves, and/or preserved lemon as desired.

Step 10

Do Ahead: Stew can be made 3 days ahead. Keep chilled.