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Cook bacon in boiling salted water 3 minutes, then drain.
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Pat beef dry and season with salt and pepper. Divide flour and beef between 2 (1-quart) sealable plastic bags, seal, then shake to coat meat.
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Heat 1 1/2 tablespoons of oil and 1 1/2 tablespoons butter in a wide 6- to 8-quart heavy pot over moderately high heat until hot but not smoking, then brown beef well on all sides in 2 or 3 batches, without crowding, adding remaining 1/2 tablespoon of oil as needed. Transfer to a bowl.
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Pour off any excess oil from pot, then add brandy to pot. Deglaze by boiling over high heat 1 minute, stirring and scraping up brown bits, then pour over beef.
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Tie celery, parsley, thyme, bay leaves, and cloves together with kitchen string to make a bouquet garni (tuck cloves into celery so they don’t fall out).
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Heat 1 tablespoon butter in cleaned pot over moderately high heat until foam subsides, then sauté bacon, stirring, 2 minutes. Add chopped onions, garlic, and carrots, then sauté, stirring, until onions are pale golden, about 5 minutes. Add tomato paste and cook, stirring, 1 minute. Add wine, meat with juices, and bouquet garni and simmer gently, partially covered, until meat is tender, 3 1/2 to 4 hours.
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While meat simmers, blanch boiling onions in boiling salted water 1 minute and drain in a colander. Rinse under cold running water, then peel.
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Heat 1 tablespoon butter in a 3-quart heavy saucepan over moderately high heat until foam subsides, then sauté boiling onions, stirring occasionally, until browned in patches. Season with salt and pepper. Add 2 cups water (1 1/2 cups if using pearl onions), then simmer, partially covered, until onions are tender, 15 to 20 minutes. Boil, uncovered, stirring occasionally, until liquid is reduced to a glaze, 5 to 10 minutes.
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Heat remaining tablespoon butter in a large nonstick skillet over moderately high heat until foam subsides, then sauté mushrooms, stirring, until golden brown and any liquid mushrooms give off is evaporated, about 8 minutes. Season with salt and pepper.
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Stir onions and mushrooms into stew and cook 10 minutes. Remove bouquet garni and skim any fat from surface of stew. Season with salt and pepper.
