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1
Set a wide, heavy pan over high heat and add the butter for sautéing. When the foam subsides and the butter is fully hot, add the quartered mushrooms — in batches if the pan would be crowded. The correct signal is an immediate, aggressive sizzle that sustains. If that sizzle dies within ten seconds, the pan is too cold or too full: remove the mushrooms, raise the heat, and begin again. Sauté until the edges are golden and a Maillard-browned fond has formed on the base of the pan.
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2
Reduce the heat to medium. Add the finely minced shallots to the pan and soften them briefly in the residual butter and mushroom fat, stirring to lift any fond. The shallots are ready when translucent and fragrant but not coloured.
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3
Pour in the white wine. Raise the heat and reduce by half. The smell moves from sharp and alcoholic at the outset to sweeter and more complex as the alcohol drives off and the shallot sugars concentrate — that shift in aroma marks the reduction's completion.
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4
Add the tomato concassée or dissolved tomato paste. Simmer for 5 minutes. The sauce takes on a warmer colour and the raw acidity of the tomato mellows.
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5
Add the demi-glace. Simmer together for 10 minutes. The sauce is ready when it coats a spoon in a rich, even layer — brown, with the mushroom pieces distributed throughout, lighter in tone than a bordelaise.
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6
Remove the pan from the heat. Mount with the cold butter, swirling or whisking until fully incorporated and the sauce carries a slight sheen.
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7
Add the freshly chopped tarragon and flat-leaf parsley. The herbs must go in off heat and immediately before service — never while the sauce is boiling. Taste before the herbs and again immediately after: the tarragon's anise-brightness and the parsley's green freshness should transform the sauce decisively. If that contrast is not dramatic, the herbs have been added too early on a previous attempt or are not sufficiently fresh.