Pound the flank steak to 3/8-inch thickness, trying to form a rectangle.
Combine the basil, parsley, olive oil, and pignoli nuts in a food processor until smooth. Spread mixture over the meat, leaving a 1-inch border.
Combine ground beef with beaten egg, garlic, bread crumbs, milk, and grated cheese. Set aside.
Spread slices of prosciutto over the pesto mixture, followed by the ground beef mixture, and topped with the sliced pancetta. Place the 4 partially boiled eggs down the center, flanked by the cheese logs. Roll the flank steak into a log, tie with butcher's twine, and season with salt and pepper, to taste.
Heat a few tablespoons olive oil in a large, heavy saucepan over medium-high heat. Add the meat and sear on all sides. Remove the meat from the pan and add the onions and saute until transluscent. Deglaze the pan with red wine, and return the meat to the pan. Add the tomato sauce and beef stock. Bring to a boil, then reduce to a simmer and cook for 1 hour over low heat. Alternatively, cook in a preheated 350 degrees F oven for 1 hour. Remove the falsomagro from the pan and set aside to let rest. Continue cooking sauce over high heat for a few minutes, until reduced to desired consistency. Season sauce, to taste.
Cut the meat in slices and serve with the sauce drizzled over top and with smothered greens and roasted potatoes or fettucine on the side.
Recipe courtesy of Chef Sal Passalacqua, Dimaio Cucina