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1
Sweat the shallots in a wide, deep sauté pan over low heat until softened and translucent but without colour. Add the bouquet garni and white peppercorns, pour in the full bottle of Aligoté, and bring to a bare simmer. The liquid must register 78–80 °C on an instant-read thermometer before any fish is added; it must never boil.
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2
Lower the eel sections into the court-bouillon. Maintain the temperature strictly at 78–80 °C throughout. After 8 minutes, add the pike portions. At 12 minutes from the start, add the tench. At 18 minutes, lay in the perch fillets. Continue poaching until 25 minutes total have elapsed from the moment the eel entered the liquid. Every species should be just yielding to a fine skewer with no resistance, and all reach this point simultaneously — this sequenced addition is where the dish lives or dies.
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3
Lift the fish carefully from the liquid with a slotted spoon or fish slice and hold, covered, in a warm place. Strain the court-bouillon through a fine sieve into a clean saucepan, pressing lightly on the solids. The strained liquid must be clear and amber-gold; discard all solids.
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4
Reduce the strained cooking liquid over moderate heat until halved in volume. Lower the heat to the gentlest possible flame. Begin adding the cold butter piece by piece, whisking constantly, incorporating each piece fully before adding the next. The pan must never exceed 63 °C — keep one hand cupped around the base of the pan to monitor the heat. The finished beurre blanc is creamy, fully emulsified, and coats the whisk with a pale, glossy film.
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5
Fry the bread slices in butter over moderate heat until deep golden on both sides. Remove from the pan and immediately rub each surface with the cut face of the garlic clove. The croûtons should be crisp throughout and carry a distinct, savoury garlic scent.
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6
Arrange portions of each fish species in deep warmed plates so that the variety is visible. Nap generously with the beurre blanc. Place the croûtons around the fish. Serve at once.