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1
Melt the butter in a wide sauté pan over medium heat. Add the sliced onions with a pinch of salt and sweat slowly, stirring occasionally, until fully softened and golden but not coloured — the onions must lose all raw bite without taking on any brown caramel tone. The test: a piece pressed between finger and thumb offers no resistance.
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2
Pour in the white wine and raise the heat. Reduce by two-thirds, stirring once or twice, until the liquid is syrupy and the sharp alcohol smell has entirely left the pan. The test: the scent is round and vinous, with no harsh edge.
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3
Add the demi-glace, stir to combine, and simmer over low heat for 20 minutes. This is the step on which the dish lives or dies: the demi-glace must reduce and marry with the onion-wine base until the sauce coats the back of a spoon thickly enough to hold a clean line drawn through it — under-reduced and it will run off the chop; over-reduced and the mustard will break on contact. The sauce is not strained at any point; the softened onions remain, giving the finished sauce its characteristic body and rustic texture.
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4
Add the cornichon julienne and the brine splash to the simmering sauce. Cook for exactly 2 minutes — no longer. The test: the cornichons are warmed through and their brine scent rises from the pan, but they retain their snap; a ribbon pressed lightly still pushes back.
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5
Remove the pan entirely from the heat. Whisk in the Dijon mustard in one motion until fully incorporated. The test: the sauce is glossy, uniformly tan, with visible ribbons of cornichon and islands of soft onion — it must not return to the heat after this point, or the mustard will turn harsh and grainy.