Set the lamb shoulder in a large roasting pan or baking dish.
In a small bowl, mix the salt with the sugar, pepper, cumin, cinnamon, and sumac. Rub the mixture all over the lamb and transfer to the refrigerator. Let sit, uncovered, overnight. The next day, retrieve the lamb from the refrigerator and discard any liquid that accumulated in the container. Using clean paper towels, dry the lamb well. Using butcher’s twine, roll up and tie the lamb. Let sit out until it comes to room temperature, 1-2 hours.
Preheat oven to 300°F. Set a large Dutch oven over high heat. Add 3 tablespoons olive oil and heat until shimmering, about 90 seconds. Lower the heat to medium-high and add the lamb shoulder; let cook, rotating as needed, until well-seared on all sides, about 8 minutes. (Be careful about temperature: the spices burn easily if the pot becomes too hot.)
Remove the lamb to a clean plate. Discard all but about 3 tablespoons of fat from the pan. Lower the heat to medium-low and add the carrots, onion, garlic, cilantro, preserved lemon, and a pinch of kosher salt. Cover and let the vegetables steam a little, stirring every few minutes, until tender, about 5 minutes. Add the stock and the rose water. Carefully return the lamb shoulder along with any resting juices to the pot. (The liquid should only come partially up the side of the lamb shoulder.)
Bring to a simmer, top with a round of parchment paper, and cover with the lid. Transfer to the oven and cook until the lamb is tender but not falling apart, about 2 ½ hours. (You should be able to poke through with a skewer, and feel just a little resistance.)
Retrieve the lamb from the oven and remove the lid and the parchment. Transfer the lamb to a large plate and set aside.
Add the turnips and carrots to the pot and return the pot to the oven, uncovered. Cook until the vegetables are softened, but still maintain a bit of their integrity, about 30 minutes. Retrieve the pot from the oven and stir in the turnip greens if using. Return the lamb to the pot and bake again, uncovered, to heat the lamb through, 10 minutes.
Remove and transfer the lamb to a clean cutting board. Cut away the twine and slice the lamb into thick slices. (They may fall apart slightly.)
Add the braising liquid to a shallow serving bowl and stir in the lemon juice. Add the sliced lamb. Top with a drizzle of pistachio or olive oil, the chopped pistachios, and some rose petals and finishing salt to taste.