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1
Place the egg yolks and Dijon mustard in a bowl. Whisk together until the mixture is homogeneous and slightly pale. Begin adding the oil in a very fine stream — no faster than a thin thread — whisking constantly, until the emulsion takes. Once half the oil is incorporated and the mayonnaise is visibly thick and glossy, the remainder may be added in a slightly steadier pour. Season with lemon juice and fine salt. The mayonnaise is ready when it holds a firm ribbon that does not dissolve back into itself.
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2
In a mortar, pound the anchovy fillets with the garlic clove and a few nonpareil capers to a smooth, unified paste. No visible filament or chunk of anchovy should remain. This is the step on which the dish lives or dies: an improperly broken-down anchovy will give isolated fishy intrusions rather than the seamless background umami the sauce requires. The paste is ready when it is grey-brown, homogeneous, and slides cleanly from the pestle.
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3
Work the anchovy-garlic paste into the prepared mayonnaise base with a spatula. If using anchovy essence, add it now. Fold until fully absorbed and no streaks remain. The sauce should deepen slightly in colour and carry a perceptible savoury weight on the nose.
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4
Fold in the remaining capers, finely chopped cornichons, parsley, chervil, and tarragon by hand. Do not whisk — the herbs and capers must remain intact. The finished sauce should be a pale greenish ivory, speckled throughout with herb and caper. Taste: mustard heat, salt, brine, herb fragrance, and umami must each be present and no single element may dominate.
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5
Transfer to a sealed container. Hold at 4 °C and serve within 6 hours of preparation. The sauce is ready to serve when it has rested at least 15 minutes and the flavours have knitted together — the mustard bite should be present but no longer sharp and raw.