Cook's Note: The sweetbread hearts are the round sweetbreads that surround the heart of the animal. Thymus gland sweetbreads are longer and thinner in shape.
For the sweetbreads ragu: Melt the butter in a large cast-iron casserole dish. Add the mushroom trimmings, garlic, celery, bay leaf, carrots, leeks, onions and cook over medium heat until nice and tender but not caramelized or colored, about 5 minutes. Pour in the wine and cook until the liquid has completely reduced and is almost gone. Pour in the chicken stock and bring to a boil.
Rinse off the sweetbreads in cold water to remove any excess blood and gristle, and then add to the braising liquid and poach for 10 minutes. Turn off the heat and let cool enough to handle before removing and breaking into bite-size pieces.
Strain the cooking liquid through a fine mesh sieve into a clean pan and cook until reduced by half to create a heavily-flavored viscous broth.
For cooking the pasta: Bring a large pot of salted water to a boil. Meanwhile, add 1 ounce of the butter and the mushrooms to a large frying pan and saute. Add the sweetbreads ragu and continue cooking until slightly browned. Pour in some of the reduced sweetbreads broth, reduce the heat to low and add the remaining butter.
Blanch the fresh Egg Pasta for about 45 seconds, and then strain, reserving some of the cooking water. Add the pasta to the sweetbreads and mushrooms and cook in the broth for another 45 seconds. Stir in the Parmesan and parsley. If the sauce looks too thick, add a touch of the reserved cooking water. Season with salt and pepper and a drop or two of lemon juice, if desired.
Serve in a large bowl and garnish with the prosciutto and a little more grated Parmesan.
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Combine the flours in a food processor and pulse for about 30 seconds, and then pour in the olive oil and pulse for another 30 seconds. Add the eggs yolks and the eggs in a constant stream while the machine is running and pulse until well incorporated.
Turn the mixture out onto the tabletop and knead until you have a smooth ball of dough, at least 5 minutes. Wrap in plastic wrap and refrigerate for at least 30 minutes, or up to 12 hours.
Roll out the dough using the recommended instructions for your pasta roller, and then cut with the capellini attachment.