Special equipment: A ricer
Prepare lamb: Preheat the oven to 350 degrees F. Heat the oil in a Dutch oven over medium-high heat. Season the lamb shanks with salt and pepper and brown them in batches, transferring each to a plate when browned. Add onions and herb sprigs and cook, stirring, until lightly browned and soft, about 10 minutes. Return the shanks to the Dutch oven with the wine, broth, and water and bring to a boil. Cover, transfer to the oven, and braise until fork tender, about 2 hours. Transfer shanks to a plate. Discard herb sprigs. Pour cooking liquid (including onions) into a large glass measure.
Prepare potatoes and boil carrots while lamb roasts: Pierce each potato once with a fork and bake on rack in lower third of oven until cooked through, 45 to 50 minutes. Cool potatoes 10 minutes, then halve lengthwise and scoop out flesh. Force warm potatoes through ricer into a bowl. Stir in milk, and salt, pepper, to taste.
Cook carrots in boiling salted water until tender, about 10 minutes. Rinse under cold running water to stop cooking.
Make gravy: Skim fat from cooking liquid (you'll have about 2 1/2 cups broth). Put the cooking liquid in a saucepan and bring to boil. Knead the flour and softened butter into a paste and whisk it into the liquid. Return the gravy to a boil to thicken and simmer, whisking occasionally, for 5 minutes.
Cut lamb meat from bones, then tear meat into bite-size pieces. Stir meat into gravy and set aside.
Assemble and bake pie: Spoon lamb-shank mixture into a 12 by 3-inch oval gratin dish or a 2 1/2 to 3-quart shallow baking dish, spreading evenly. Scatter carrots over lamb, then top with creamed spinach, spreading evenly. Top spinach with mashed potatoes, spreading evenly to edges of dish to cover filling completely. Make swirl patterns on surface of potatoes with back of spoon, then drizzle with the melted butter.
Put baking dish in a foil-lined shallow (1-inch-deep) baking pan to catch drips and bake until top is golden and filling is bubbling, about 1 hour.
Cook spinach according to package directions. Whisk in Parmesan, salt, nutmeg, and pepper, to taste. Cook's Note: Spinach can be made 1 day ahead of assembling shepherd's pie and chilled, covered. Bring to room temperature before proceeding.