Soak the pistachios in a container of cold water for 24 hours in the refrigerator, changing the water twice. Drain, spread on a clean kitchen towel, pat dry, and remove any skin that remains stuck to the kernels. In a Dutch oven, heat 3 tablespoons oil over medium heat and brown the onions and meat. Add the salt, pepper, and turmeric. Sauté for 2 minutes. Pour in water—3 cups for lamb and 2½ cups for chicken—and bring to a boil. Cover and simmer over low heat—1½ hours for lamb and 30 minutes for chicken—stirring occasionally. Add the verjuice, saffron-rose water, and pistachios, and bring back to boil. Preheat the oven to 350°F (180°C). Transfer the braise to a deep, ovenproof casserole, cover, and place in the middle rack of the oven. Bake for 30 to 45 minutes until the lamb is tender.

Just before serving, adjust seasoning to taste, adding more verjuice or salt. Add the dill. Serve with steamed rice and a fresh herb platter on the side.