Salt the beef, cover it with plastic wrap, and refrigerate it overnight.
The next day, in a medium saucepan, cover the beef with 6 cups water. Add the wine, the peppercorns, carrots, onions, and cloves and bring to a boil. Reduce the heat to maintain a simmer and cook until the beef is tender, 1 1⁄2 to 2 hours. Transfer the meat to a plate and shred it with tongs or two forks and transfer it to a food processor. Strain the broth through a fine mesh sieve over a bowl and discard the solids.
Meanwhile, in a small saucepan, boil the potato until tender, about 40 minutes. Transfer to a bowl and, when cool enough to handle, peel and cut into 1-inch pieces. Add the potato and mortadella along with 1 to 2 tablespoons of the reserved broth to the food processor and pulse until it forms a paste. Transfer to a medium bowl along with the Parmigiano-Reggiano, parsley, and half of the eggs. Season with salt and pepper and mix well to combine. Refrigerate 1 hour.
Remove the beef from the refrigerator and form into 16 patties, about 2 1⁄2-inches wide and 1⁄2-inch thick. Heat 2-inches vegetable oil in a 6-qt. saucepan until a deep-fry thermometer reads 350°. Place flour, remaining eggs, and bread crumbs in separate shallow dishes. Working with 1 patty at a time, dredge in flour, dip in eggs, and coat in bread crumbs. Working in batches, fry patties until golden and crisp, 3 to 4 minutes. Transfer patties to paper towels to drain and serve hot.