Fill a very large stockpot about halfway with water, and add the aromatics and bring to a boil. Let the aromatics cook for 15 minutes.
[NB: If you don't have a pot big enough to handle the various cuts of meat, you can use separate pots. In fact, some of the secondary meats, especially those that are quite fatty and/or strongly flavored like the tongue and the cotechino, are usually cooked separately anyway. Some recipes call for you to cook the hen or chicken separately as well, so as not to mix different flavors.]
How begin adding your meats in the order that they usually take to cook, starting of course with those that take the longest. Here is a list summarizing typical cooking times: 3-1/2-4 hours : Beef hoof, ox tongue; 3-3-1/2 hours: Brisket, chuck, bottom round, rump, shank, ribs and short ribs, oxtail; 2-2-1/2 hours: Veal tongue, hen, calf's head, large cotechino/zampone, veal trotter; 1 or 1-1/2 hours: Chicken, small cotechino; 1/2 hour: Pre-cooked cotechino
Calculate things so that everything will be done at the same time. So, for example, if you were cooking brisket, tongue and a chicken, you would start with the brisket, start the tongue an hour later and then the chicken an hour later and cook for an hour more.
Start the water off at a brisk boil, but after that maintain a steady but gentle simmer, skimming off any scum that comes to the surface as you need to and topping the pot up with more water if too much cooks off. If one meat is tender before another is done, just remove it from the pot into a bowl, moisten it with some broth from the pot, and cover it loosely; add it back to the pot at the end to reheat. Once cooked, the meats can stay off heat (or on minimal heat) almost indefinitely, until you are ready to serve.
[NB: If cooking veal or ox tongue, you will need to remove it when it's done and skin it. Then return the tongue to broth to re-heat before serving. See our post on Gratinéed Ox Tongue in Mushroom Cream Sauce for details.)
While the meats are simmering, they need little attention, and you can get on with the business of preparing sauces and sides.
When you are ready to serve, lay out the meats on a large, pre-heated platter. Ladle over some of the broth to moisten the meats. Bring the platter to the table, along with the sauces and sides, and slice the meats at table for each of your guests.