Clean the brains and the sweetbreads under cold running water, removing membranes and veins.
Bring a pot of lightly salted water to a boil and cook the sweetbreads, cockscombs, wattles, and testicles for 10-15 minutes, until they can be easily peeled. Remove the pot from the fire, peel the membranes from the meats, and return th peeled pieces to the salted water to keep them from discoloring.
In a second ample saucepot bring lightly salted water flavored with vinegar and the parsley to a boil and blanch the brains and marrow. Cook for 10 minutes, and then drain.
Chop all the meats, and the cucumber (into a smaller dice), and the mushrooms, and lightly flour the meats.
Heat the butter in a saucepan, and simmer everything for 10-15 minutes over a gentle flame, stirring often. Add the Marsala, simmer 10-15 minutes more, and it's ready.
In terms of serving suggestions, the Finanziera is traditionally used to fill puff pastry vol-au-vents, and is also served as an accompaniment to vegetable sformati or even rice. A wine? Nebbiolo d'Alba will be good, and so will either Ruché or Pelaverga di Verduno, two richly aromatic Piemontese reds.
Notes and Variations:
This is an old, old dish, first mentioned by Maestro Martino in the 1450s, and there are a great many variations.
Alessandro Pradelli suggests peas (a half cup), or egg and freshly grated Parmigiano Reggiano (the egg lightly beaten and mixed into the cheese,a nd all stirred in at the end to thicken the finanziera) if the finanziera is to be used to fill puff pastry shells.
He also notes that some people sauté onion and garlic in the butter before adding the meats, and that others add minced parsley and lemon juice to the meats after the Marsala has evaporated, and I have seen other recipes that have you add a little vinegar at the end rather than lemon juice.
Giovanni Goria instead says the addition of peas to a finaziera is scellerato, or nefarious. He does admit the addition of a few well-rinsed pickled capers and chopped pickled mushrooms, and also says that one can add chicken giblets and hearts, well washed, blanched, and peeled (the giblets), or rabbit organs.
Other recipes say to boil a carrot and a half a head of cauliflower in lightly salted water too, and to finely dice them -- the pieces should be smaller than those of the meats -- and add them when simmering the combined meats.