Cut the shoulder meat into 1 1/4-inch cubes and trim off the large chunks of fat. Place the fat in a heavy pan or Dutch oven over mediumlow heat and cook until the fat runs out, about 5 minutes. Discard any solid bits of fat that remain.

Season the meat with salt and pepper and add to the hot fat. Brown meat on all sides, working in batches if necessary, about 5 minutes per batch. Transfer browned meat to a casserole. Add the onions, leeks, swedes, and turnips to the pot, season with salt and pepper, and brown lightly in the fat. Add the vegetables to the casserole. Pour the stock into the pan, bring to a boil, and stir to dissolve the caramelized bits. Pour into the casserole. Lay the potatoes over the vegetables in the casserole, season with salt and pepper, and bring to a boil over the stove.

Cover the casserole, reduce heat to medium-low, and simmer until the lamb is tender and vegetables are cooked, stirring occasionally, about 1 hour.

When stew is cooked, pour off cooking liquid into a clean saucepan. Skim off any excess fat and bring liquid to a simmer. In another saucepan, make a roux by melting the butter, then whisking in the flour until it forms a smooth paste. Cook roux over low heat for 2 minutes. Add roux to cooking liquid, whisking until thickened slightly. Add parsley and chives, taste for seasoning, and pour back over casserole. Bring casserole back up to a simmer and serve immediately.