For the stew
2 tablespoons olive oil
2 1/4 to 2 1/2 pounds boneless lamb shoulder or leg meat, cut into 1 1/2-inch chunks
4 1/2 teaspoons kosher salt, divided, plus more as needed
1 tablespoon ground Aleppo or Marash pepper, plus more as needed
1 tablespoon ground cumin
1 teaspoon ground anise seeds (optional)
15 cloves garlic, minced
1 1/2 cups beef or lamb broth
4 cups sliced button or cremini mushrooms (about 1 pound)
4 large leeks (about 3 pounds), washed well and thinly sliced (3 1/2 to 4 cups)
2 medium or 1 large celery root (about 1 1/4 pounds), peeled and cut into 1/2-inch chunks (about 2 cups)
1 small head cauliflower, trimmed and cut into small florets (about 1 1/2 cups)
6 medium carrots (about 1 pound), trimmed, peeled, and cut into 1/2-inch chunks (about 1 1/2 cups)
Leaves of 1 large bunch fresh mint, finely chopped
1 1/2 cups roasted red peppers (from a 12-ounce jar), drained
1 1/2 cups blanched, slivered almonds
For the topping
5 cups mashed potatoes, warmed
Finely grated zest of 2 large lemons
1/4 cup blanched, slivered almonds
Make the stew: Heat the oil in a 6-quart or larger Dutch oven over high heat until shimmering. Add the lamb, arranging it in a single layer. Sprinkle with 2 1/2 teaspoons of the salt and the Aleppo or Marash pepper and cook until the meat is seared and browned, 2 to 3 minutes.
Add the cumin and anise, stir to combine, and cook for 15 seconds. Add the garlic and broth and stir to combine, scraping up any browned bits from the bottom of the pot.
Reduce the heat to a simmer and add the mushrooms, leeks, celeriac, cauliflower, carrots, remaining 2 teaspoons of salt, and mint and stir to combine. Cover and cook until the vegetables are completely soft and the meat is fork-tender, 4 to 4 1/2 hours. Liberally skim the fat and any accumulated scum off the top of the stew as it is cooking. (Alternatively, use a slow cooker. See Recipe Notes below.)
Transfer about 1 cup of the stew cooking liquid to the bowl of a food processor fitted with the blade attachment or a blender. Add the red peppers and almonds and process or blend until smooth and creamy. Transfer the mixture into the stew and stir to combine; set aside.
Arrange a rack in the middle of the oven and heat to 425°F. If you used a slow cooker to prepare the stew, coat a deep 13x9-inch baking dish with cooking spray and transfer the stew into it, spreading it in an even layer. If you used a Dutch oven, you can continue this dish in it.
Make the topping: Transfer the mashed potatoes to a large bowl. Add the lemon ze