Preheat oven to 275°F.
In a large skillet melt 2 tablespoons of the butter with 1 tablespoon of the oil over high heat. Season one-third of the lamb with the salt and pepper. Brown the lamb on all sides until lightly crusted, about 10 minutes. Transfer to a large casserole or Dutch oven and set aside. Pour off the fat from the skillet. Add 1 cup of stock and bring to a boil, scraping up the browned bits that adhere to the pan. Pour into the casserole with the lamb. Repeat with the remaining lamb, using 2 tablespoons butter and 1 tablespoon oil for browning each batch and deglazing with 1 cup broth.
Add the remaining 1 cup stock with the optional scotch, sage, and thyme. Cover and bake for 1½ hours. Remove from the heat, uncover, and cool to room temperature. When cool, cover and refrigerate for 24 hours.
Preheat the oven to 300°F. and remove the casserole from the refrigerator. Skim off the film of cold fat on the surface. Cover the casserole and bake for 30 minutes while you prepare the vegetables.
In a pot of lightly salted boiling water, cook the potatoes for 10 minutes until slightly resistant when pierced with a knife. Transfer the potatoes with a slotted spoon to a bowl and set aside. Add the carrots to the boiling water and cook for 4 minutes until slightly resistant when pierced with a knife. Drain and set aside. When the stew has baked for 30 minutes, add the partially cooked potatoes and carrots and bake for an additional 30 minutes.
Meanwhile, trim the onions and cut an “X” into the root end of each. Bring a pan of lightly salted water to a boil. Add the onions and cook until tender, about 8 minutes. Drain and rinse them under cold running water. Drain again and remove the outer skins. Set aside.
Peel the turnips and halve into ¼-inch wedges. Bring a saucepan of lightly salted water to a boil. Add the turnip wedges and cook until crisp-tender, about 4 minutes. Drain and rinse under cold running water. Drain again and set aside.
In a medium sauté pan, melt the remaining 2 tablespoons of butter over medium heat and add the onions and turnips. Sprinkle with the sugar and continue to cook, tossing often, until the onions and turnips are golden and caramelized, about 10 to 15 minutes.
To serve, ladle the stewed lamb, potatoes, carrots, and some of the sauce onto warm plates or soup plates. Divide the onions and turnips among the plates and sprinkle with the parsley.