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1
Make the egg pasta by combining the 00 flour and eggs on a clean surface, working them to a smooth, elastic dough, then wrapping and resting for at least 30 minutes so the gluten relaxes and the sheets will roll without springing back. Roll out on the thinnest setting of a pasta machine — the sheets must be very thin, almost translucent, because thicker sheets will stay dense and leathery once baked under the ragù and besciamella. Blanch in well-salted boiling water for 30 seconds, refresh in cold water, and lay flat on clean cloths; the sheets are ready when they are pliable and no longer sticky.
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2
Melt the butter in a wide, heavy pan over a moderate heat, add the prosciutto strips, and let them colour lightly so their fat renders and scents the base of the ragù before the mince goes in. Add the minced beef and pork and cook, stirring, until the meat has lost all raw colour and any liquid has fully evaporated — the pan should be beginning to sizzle rather than steam, because meat that stews in its own liquid will taste flat rather than roasted and sweet.
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3
Add the drained porcini and stir through. Pour in the white wine and allow it to reduce until the sharp vinous smell has left the pan and only a deeper, more rounded aroma remains, because wine added too briefly will leave a raw, acidic edge that no amount of later simmering will correct.
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4
Add the crushed tomatoes and the stock, reduce the heat, and simmer gently uncovered for 30 to 40 minutes until the sauce is cohesive and no longer watery. Leave the ragù quite liquid at this stage, because the besciamella assembled over and around it is thick, and together they will produce the right consistency in the finished dish rather than a dry, tight filling.
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5
This is where the dish lives or dies. Add the sweetbreads and the chicken livers to the ragù and give them no more than 5 to 10 minutes over a moderate heat — the livers should be just cooked through, still very slightly pink at the centre when pressed, because a liver even one minute past this point turns granular and bitter, losing the delicate quality that defines vincigrassi against an ordinary meat lasagne. Remove the pan from the heat the moment this point is reached.
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6
Make the besciamella by melting the butter in a heavy saucepan, adding the flour, and cooking the roux over a low heat for 2 minutes, stirring constantly, until it smells faintly of biscuit but has taken no colour — this brief cooking drives off the raw floury taste that would otherwise persist through the finished dish. Add the warm milk gradually, whisking after each addition so no lumps form, then cook, stirring, until the sauce is thick enough to coat a spoon heavily and holds a clear channel when a finger is drawn across the back of the spoon; season with salt and nutmeg.
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7
Assemble the vincigrassi in a buttered baking dish, beginning with a thin layer of besciamella on the base so the first pasta sheet does not stick and dry out during baking. Layer pasta, ragù, besciamella, and a scattering of Parmigiano-Reggiano, repeating for 4 to 5 layers in total — no more — because beyond this the dish becomes unwieldy and the layers lose their distinction. Finish with pasta topped with besciamella, Parmigiano, and the small pieces of butter; the assembled dish should be even and compact, not towering.
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8
Bake at 180 °C until the surface is golden and the edges are bubbling and slightly pulled away from the sides of the dish. Remove from the oven and rest for 10 to 15 minutes before cutting, so the layers firm and the portions hold their shape cleanly when lifted rather than collapsing into each other on the plate.