Rinse beef and pat dry. Sprinkle with cumin. Heat 1 tablespoon oil in a heavy 6- to 8-quart pot over moderately high heat, until hot but not smoking. Add beef and brown, turning, until golden brown on all sides, about 6 minutes. Transfer to a plate.

Add onion and celery to same pot; cook over moderately high heat, stirring, until onion is golden brown, about 15 minutes. Add garlic and cook, stirring 1 minute. Transfer half of onion mixture to a bowl; reserve. Add half of barbecue sauce and 1 cup water to onion mixture in pot; stir, scraping up any browned bits on bottom of pot.

Return beef to pot; cover with reserved onion mixture and remaining barbecue sauce. Bring to a simmer and cover. Simmer, stirring occasionally, adding 1/2 cup water toward end of cooking time if sauce begins to stick to bottom of pot, until meat is very tender, about 3 hours.

Meanwhile, place turnips and potatoes in a 4-quart saucepan, cover with cold water by 2 inches and bring to a boil over moderately high heat; add salt. Simmer until very tender, about 20 minutes. Reserve 1/4 cup cooking liquid and drain vegetables in a colander. Return to pot with reserved cooking liquid and the milk. Mash with a handheld potato masher until smooth. Stir in horseradish sauce and parsley. Keep warm, covered.

While vegetables are cooking, preheat oven to 425 degree F and arrange rack in lower third. Toss together brussels sprouts and remaining 1 tablespoon oil in a large shallow baking pan; season with pepper. Roast, stirring occasionally, until golden brown, about 15 minutes. Transfer to a serving bowl and keep warm, covered.

Remove beef from sauce and cut into thin slices. Spoon some onion mixture onto serving plates, top with a mound of mashed turnips and potatoes, then slices of beef and more onion mixture. Serve brussels sprouts on the side. Makes 10 servings.