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1
Blanch the sweetbreads by placing them in cold water acidulated with a splash of white wine vinegar, bringing to a gentle simmer, and poaching for 5 minutes — the acid firms the outer membrane so it peels away cleanly rather than tearing into the flesh. Drain, refresh in iced water, then peel away all membrane and connective tissue. Press between two plates, refrigerate for at least 1 hour so the lobes compact into a dense, sliceable block, then dice to 1 cm; the interior should be uniformly pale and firm with no grey patches.
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2
Make the pasta by mounding the flour on a board, breaking in the eggs, and working to a smooth, elastic dough; wrap and rest at room temperature for 30 minutes so the gluten relaxes and the sheet rolls without springing back. Roll out slightly thicker than standard lasagne sheets, as they need the body to hold the offal ragù without dissolving under the béchamel during baking. Cut to fit your baking dish with 2–3 sheets in reserve for patching tears, parboil in well-salted water for 1 minute, lift onto clean cloths, and leave flat.
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3
Build the ragù in a wide pan by melting the butter with the oil over medium heat, adding the soffritto of onion, celery and carrot, and cooking until softened and translucent so the vegetables lose their raw sharpness and sweeten into the base. Raise the heat, add the diced sweetbreads and cook until lightly coloured, then add the chicken livers and cook, stirring, until just firmed through but still faintly pink at the centre — cooking them further will make them grainy and bitter. Pour in the Marsala or Vin Santo and let it reduce almost entirely so the fortified wine's oxidative sweetness is present but no longer raw; season with salt and pepper, and the ragù is done when the pan smells of cooked offal, sweet wine, and the soffritto has dissolved into the base.
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4
Make the béchamel by melting the butter in a saucepan, whisking in the flour, and cooking for 1 minute without colour so the raw floury taste cooks out before the milk goes in. Add the warm milk in a steady stream, whisking constantly, then cook over low heat until the sauce coats the back of a spoon loosely — it must flow between layers and not set solid, so test by tilting the pan and watching it move freely but with body. Season with salt and nutmeg.
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5
Assemble the vincisgrassi by lightly buttering the baking dish, then laying a pasta sheet across the base, spreading a thin layer of béchamel, distributing a portion of the ragù, and scattering Parmigiano — keep each layer of béchamel thin and even so it lubricates rather than floods the ragù. Repeat the layers — pasta, béchamel, ragù, Parmigiano — finishing with a pasta sheet topped with béchamel, the remaining Parmigiano, and small pieces of butter scattered across the surface so the top colours evenly in the oven. The top layer should appear evenly coated with no dry patches of pasta visible.
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6
Bake in an oven preheated to 180 °C until the surface is golden and bubbling at the edges and a skewer inserted into the centre comes out hot to the touch. Remove from the oven and rest for 15 minutes before cutting — the layers set during this time and slices will hold their structure, whereas cutting too soon will see the béchamel run and the layers slide apart on the plate.
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7
Serve on plates heated as hot as the oven allows, and portion the vincisgrassi immediately. Shave the white truffle directly over each plate table-side so the first aroma rises when the truffle meets the heat of the pasta — pre-shaved truffle loses half its volatile fragrance before it reaches the guest.