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1
Slice the onions uniformly at 2 mm. Place them in a wide sauté pan with the clarified butter and a pinch of fine salt over medium-low heat. Cover the pan and allow the onions to sweat for 10 minutes; they will collapse and release their moisture. The onions are ready to move to the next phase when they are fully softened and translucent.
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2
Uncover the pan and increase the heat slightly. Continue to cook, stirring occasionally, for a further 15–20 minutes — this is where the dish lives or dies: the onions must reach a deep golden-amber caramelisation through true Maillard reaction, not coloured with sugar or rushed with high heat. Under-caramelised onions will taste of raw allium; correctly caramelised onions will smell of savoury sweetness and collapse into soft, amber ribbons. The total cooking time from start is 25–30 minutes.
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3
Add the white wine vinegar to the pan and reduce completely over medium heat, stirring to lift any deposit. The pan is ready when the vinegar is no longer perceptible by smell and the onions appear almost dry.
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4
Pour in the demi-glace and simmer gently for 15 minutes, stirring occasionally, until the sauce is fully integrated and coats the back of a spoon.
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5
For a fine-dining finish, pass the sauce through a fine sieve, pressing the onions firmly to extract all liquid. For a bistro presentation, leave the onions in the sauce. Both are classical. Adjust seasoning and serve immediately with grilled liver, sautéed potatoes, or pan-fried tripe.