Preheat the oven to 425°F.

Roast the meaty shanks in a heavy-duty roasting pan for 20 to 25 minutes, until thoroughly browned, turning once. Over medium-high heat, sauté the carrots, onions, and celery in olive oil for 5 minutes to caramelize them lightly. Put the roasted bones and 5 quarts cold water in a large stainless steel stockpot and bring to a boil. Deglaze the roasting pan with a little water, vigorously scraping with a wooden spoon, and add these flavorful pan drippings to the stockpot. When the stock comes to a full boil, skim off the gray foam. Add the carrots, onions, celery, parsley, thyme, bay, peppercorns, and, if you wish, salt. Use salt sparingly if you intend to make a reduction later—the stock will become saltier as it reduces.

Turn the heat to low and simmer very slowly for 4 to 5 hours, until the broth tastes rich and is a light caramel color. Strain through a finemesh colander or sieve. Allow the stock to cool completely; remove fat from the surface and promptly refrigerate. The stock is ready to use as is, or it may be reduced further to create a glaze or sauce.