Heat oven to 350 degrees. Place meat in a roasting pan or rimmed baking sheet and drizzle with most of the Wild Mushroom & Sage Olive Oil, reserving just a bit to mix into and thin out the tomato paste. Once mixed together, brush tomato-and-oil mixture all over the meat and roast until good color begins to develop, about 45 minutes. (Meat will not be fully cooked; color is more important than doneness at this point.)
Transfer roasted meat and bones to a large (at least 12-quart), heavy-bottomed stockpot. Add drippings from roasting pan, the Neapolitan Herb Balsamic Vinegar, and enough cold water to cover by about 3 inches, roughly 6 quarts. Bring everything to a rapid boil, then reduce heat to a gentle simmer. Continue simmering, uncovered, for 3 hours, periodically skimming fat and foam from the top.
Add the rest of the ingredients and continue to simmer, uncovered, for a bare minimum of 3 hours and up to 24; the longer, the better.
Once broth has simmered long enough for your liking, remove solid meat and vegetables with a slotted spoon or tongs and transfer to a colander set over a large bowl; allow to drain while you strain the rest of the broth.
Working in batches, pour broth through a fine-mesh strainer set over a second large bowl. Stir small solids with a spoon to move them around and allow broth to filter through as cleanly as possible; repeat process two more times, or until broth shows no more traces of solid matter. Repeat with runoff from large solids; the solids themselves can be reserved for another use, eaten, or discarded.
Once broth is strained and cooled, transfer to an airtight container and refrigerate or freeze.
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