How to Make It
Preheat the oven to 350°. In a large enameled cast-iron casserole, heat the oil. Season the pork slices with salt and pepper and brown over moderately high heat, turning once, 10 minutes. Transfer the pork to a plate.
Reduce the heat to moderate. Add the onion, carrots, celery, garlic, rosemary and sage to the casserole and cook for 1 minute. Stir in the cocoa powder and cook over moderate heat until the vegetables are softened, 5 minutes. Add the tomato paste and cook, stirring, for 2 minutes. Add the wine and cook, scraping up any browned bits from the bottom of the pot, until reduced by half, 5 minutes. Add the stock and bring to a boil.
Return the pork to the pot, nestling it into the liquid. Cover and braise in the oven until very tender, about 2 1/2 hours.
Remove the meat and pull it into large shreds, discarding any fat. Transfer the braising liquid and vegetables to a blender and puree until smooth. Return the meat and sauce to the pot and stir in the mint, parsley, crushed red pepper and butter.
Meanwhile, in a large pot of salted boiling water, cook the pasta until al dente. Drain and add the pasta to the sauce, tossing over low heat until nicely coated, about 2 minutes. Serve the pasta in bowls, passing grated Pecorino at the table.
The pork-cocoa sugo can be refrigerated for up to 5 days.