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1
Melt the butter in a heavy saucepan over moderate heat. Add the diced onion, carrot, and celery together with the 2 tablespoons of coarsely crushed black peppercorns, the bay leaf, and the thyme. Sweat gently, stirring occasionally, until the vegetables are softened and the peppercorns have released their aroma into the fat. The butter should smell warm and rounded — not sharp or acrid.
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2
Pour in the red wine vinegar and raise the heat. Reduce by three-quarters, until the vinegar has lost its aggressive raw edge and the liquid in the pan is syrupy and concentrated. This is where the dish lives or dies: insufficient reduction leaves the finished sauce aggressively sour rather than structurally acidic; the vinegar must be fully disciplined before the wine enters the pan.
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3
Add the dry red wine and reduce by half over a steady heat. The liquid should again appear syrupy, with the wine's depth now layered over the concentrated vinegar.
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4
Add the 500 ml of demi-glace. Bring to a gentle simmer and cook for 30 minutes, skimming the surface frequently. The sauce should reduce to a glossy, full-bodied consistency that coats the back of a spoon.
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5
Strain through a fine chinois into a clean pan, pressing the mirepoix firmly to extract all liquid. Discard the solids.
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6
Add the remaining 1 tablespoon of freshly crushed black peppercorns to the strained sauce. Simmer for 5 minutes. Strain once more through the chinois. The finished sauce should be deep brown; tasting it, a pronounced pepper burn should arrive at the back of the throat 2–3 seconds after contact, with a lifting acidity from the vinegar and the full savour of the demi-glace beneath.