In a large bowl combine veal, pork, prosciutto, cheeses, garlic, fennel, artichokes, herbs, egg, Italian seasoning, salt and pepper and mix well. Trim excess fat from flank steak and pound to approximately 1/8 - thickness.(This takes a few minutes, but it is important to the recipe. Use a kitchen mallet or a heavy flat weight such as a wine bottle.) Spread stuffing over meat, covering it completely. Lay egg quarters down center, lenghtwise, and roll meat around stuffing without overlapping. Tie with kitchen string at one-inch intervals to hold securely; if any stuffing escapes, carefully push back in.
Heat a large heavy skillet over medium-high heat. Add 1/4 cup of the reserved artichoke oil. Heat oil and add stuffed beef roll to hot oil and brown on all sides. Add wine, cover and cook over low heat for 45 minutes. Turn beef roll over halfway through cooking. When cooked, transfer meat to a serving platter and remove the string. Slice and serve with the pan juices. The Falso Magro roll is also terrific served on buffets, at picnics or even cold the next day.