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1
Bagnet ross (make first, up to one day ahead). Combine the tomatoes, celery, carrot, grated horseradish, vinegar, and sugar in a heavy saucepan. Cook over moderate heat, stirring occasionally, until the sauce is thick, cohesive, and pulls from the sides of the pan — agrodolce, neither watery nor jammy. Pass through a coarse sieve. Reserve.
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2
Bring five separate, generously salted pots of water to a full rolling boil, each with its aromatics already in. Commit each element to its own boiling pot in the following order, staggered so all finish together: beef (3 h), tongue (2.5 h), cotechino (2.5 h), testina (2 h), chicken (1.5 h). This is where the dish lives or dies: every element must enter already-boiling water. Meat lowered into cold water surrenders its proteins to the broth and emerges grey and flavourless; meat lowered into boiling water seals immediately and holds its depth. Adjust each pot to a steady, gentle simmer once the meat is in — a vigorous boil toughens.
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3
After 20 minutes of simmering, peel the tongue: remove it briefly from its pot, slit the skin at the root with a paring knife, and strip the skin away cleanly while the tongue is still hot. Return it immediately to its pot and continue cooking for the remaining time. The skin should slide free without tearing the flesh beneath.
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4
Bagnet verde (make no more than 1 hour before service). In a mortar, pound the garlic and anchovies to a paste. Add the capers and pound to a coarse, grainy consistency. Work in the parsley a handful at a time, pounding — never blending — until the mixture is rough but unified. Stir in the red wine vinegar, then the olive oil. The sauce is ready when it holds together loosely, smells fiercely of raw parsley and anchovy, and shows a coarse, uneven green — not a smooth purée.
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5
Test each element for doneness in turn. The beef and veal are done when a thin skewer withdraws without resistance and the juices run clear amber, not pink. The chicken is done when the leg joint moves freely and the juices at the thigh run clear. The cotechino is done when it feels uniformly yielding when pressed gently — firm but not hard. The testina is done when the roll feels completely soft and gelatinous under light pressure.
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6
Arrange a deep, wide vessel of very hot water (bain-marie) at the table or on the serving trolley. Transfer each element, whole and still in its cooking liquor if possible, to the bain-marie. The water temperature must be hot enough to hold the meats — not cook them further. Meats left over direct heat become dry; the trolley is a holding and theatrical space, not a second cooking vessel.
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7
Carve each element at the trolley: slice the beef and veal across the grain in generous cuts; halve the chicken at the joint; slice the tongue thinly on the bias; cut the cotechino into coins; slice the testina so each portion shows the gelatinous layers. Serve the three sauces — bagnet verde, bagnet ross, and freshly grated cren — in separate bowls alongside.