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Heat oil in a medium Dutch oven or large saucepan over medium. Add the pancetta and cook until the fat has rendered, about 6 minutes. Using a slotted spoon, transfer the pancetta to a medium bowl.
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Season the pork with salt and pepper. Add the pork to the Dutch oven, in batches, if necessary. Cook over medium-high until richly browned all over, about 5 minutes. Using the slotted spoon, transfer the pork to the bowl with the pancetta.
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Wrap the sage, thyme, and rosemary in cheesecloth and tie with kitchen twine. Add this bundle to the Dutch oven along with the onion, carrot, celery, leek, and garlic; cook, stirring, until the onion is translucent, about 2 minutes. Stir in the wine, scraping up any browned bits on the bottom of the Dutch oven, and bring to a boil. Return the pancetta and pork shoulder to the Dutch oven and simmer over medium-low until liquid is almost fully evaporated, about 10 minutes. Add the stock and tomato puree and return to a boil. Cover and simmer the sauce over moderately low heat for 1 hour, until the meat is very tender.
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Bring a large pot of salted water to a boil. Add the pasta and cook until al dente; drain. Skim the fat from the surface of the sauce and discard the herb bundle. Season the sauce with salt and pepper. Add the pasta and toss until well-coated. Transfer to shallow bowls and serve right away, passing grated pecorino at the table.