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1
Melt the butter in a heavy-bottomed pot over medium heat. Add the sliced onions and a generous pinch of salt. Cook for approximately 15 minutes, stirring occasionally, until the onions have released their moisture and softened. The pan should be steaming and the onions collapsed and translucent — no colour has formed yet.
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2
Reduce the heat to medium-low. Continue to cook for 45 to 60 minutes, stirring every 5 to 7 minutes and scraping the fond from the bottom of the pot, dissolving it back into the onions each time. Deglaze periodically with small splashes of water or dry white wine whenever fond threatens to scorch. This is where the dish lives or dies: the onions must progress through golden to deep amber to a rich, dark mahogany — sweet, dense, and deeply complex. No heat may be raised to accelerate this; impatience produces bitter, burnt onions, not caramelisation. The onions are ready when they are uniformly dark mahogany and the pot smells of deep, sweet savouriness.
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3
Deglaze the pot with the 150 ml of dry white wine or cognac, scraping every trace of fond from the base. Add the beef stock and bouquet garni. Bring to a simmer and cook, uncovered, for 20 minutes. The broth should be a deep, mahogany colour with a full, onion-rich body.
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4
Remove the bouquet garni. Season with salt, pepper, and a splash of sherry vinegar to sharpen the sweetness. Taste: the broth should read as sweet, savoury, and sharp in equal measure.
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5
Ladle the soup into ovenproof crocks. Float one or more thick, very dry toasted baguette croûtons on the surface of each. Cover each bowl generously with 100 g of grated Comté or Gruyère, ensuring the cheese reaches from rim to rim.
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6
Place the crocks under a blazing grill. Gratinée until the cheese bubbles fiercely, browns in spots, and forms a sealed, molten cap bridging the rim of each crock. The surface should be a deep golden-brown with darker patches — not merely melted. Remove and serve immediately.