Preheat 400 degrees F. Place a large pot of water over high heat and bring to a boil.
Mix meat with the grated onion, 3 cloves chopped garlic, egg, bread crumbs, cheese, allspice, capers, sage, a handful of the chopped parsley, salt and pepper and a healthy drizzle of extra-virgin olive oil. Mix meat, score the meat into 4 sections and make 3 very large balls from each section. Arrange the 12 balls on a nonstick cookie sheet and roast 15 minutes until firm but not hard.
Drop bucatini in salted boiling water to cook off. Drain.
Add another tablespoon of extra-virgin olive oil to the skillet and the pancetta. Cook 3 to 4 minutes then add the remaining garlic and mushrooms to the pan and cook 5 minutes. Season the mushrooms with salt and pepper. Add remaining chopped onion and deglaze the pan with wine, cook off 1 minute, add in stock and whisk up remaining drippings. Stir in the tomatoes and season sauce with salt and pepper, if necessary. Stir in parsley. Simmer 5 minutes.
Toss pasta with half the sauce. Remove balls from oven and add to remaining sauce and turn to coat. Serve large balls, 3 per person, along side pasta. Spoon any remaining sauce over the pasta. Pass extra cheese at the tables.