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1
Combine the water, white wine, diced carrot, diced celery, diced onion, sliced fennel, bouquet garni, white peppercorns, star anise, lemon zest, and salt in a wide saucepan. Bring to a gentle simmer — never a rolling boil, which clouds the liquid and draws bitter compounds from the vegetables — and hold at a bare simmer for 20 minutes. The vegetables are done when they are tender but still holding their shape; they will serve as garnish.
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2
Maintain the nage at 70–75 °C — verify by thermometer. This is where the dish lives or dies: above this temperature the proteins in shellfish and delicate fish seize and toughen irreversibly. Add the chosen protein and poach for the prescribed time (langoustines 4–5 minutes; scallops 2–3 minutes; lobster tails 8–10 minutes). Remove the protein and keep warm. Lift out the vegetable garnish with a slotted spoon and reserve separately.
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3
Strain the remaining nage through a fine sieve into a smaller saucepan. Reduce over a moderate flame until the volume is halved. The liquid is sufficiently reduced when it is a translucent gold and the aromas of tarragon, fennel, and wine are concentrated but not sharp.
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4
Remove the pan from the heat. Add the cold butter piece by piece, swirling the pan continuously rather than stirring with a spoon. The butter emulsifies into the reduced nage, yielding a sauce with body and a distinct gloss. It is ready when the surface shines and the sauce coats the back of a spoon lightly — taste for salt at this point, adjusting with caution, as reduction will have concentrated the seasoning.
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5
Set wide, shallow bowls in a warm oven for a minute to take the chill off. Arrange the protein in the centre of each bowl. Scatter the reserved vegetable garnish around it. Pour the finished nage around — not over — the shellfish or fish, so the protein sits in a shallow pool. The sauce should be translucent gold, aromatic with tarragon and fennel, and taste of the sea refined through butter.