Place the flour and egg/milk mixture in separate, shallow bowls. Combine the breadcrumbs, oregano, paprika, cayenne, salt and pepper in a third bowl. Heat the oil in your deep fryer to 350 degrees F. Preheat the oven to 200 degrees F.
Pat the cheese dry with paper towel. Coat bocconcini balls in the flour, and then thoroughly coat in the egg mixture. Now coat the cheese in the breadcrumb mixture. Set cheese on a plate. Now, coat each piece of cheese in the flour, egg mixture and breadcrumbs again.
Deep-fry bocconcini, in batches, until golden, about 2 minutes. Drain well and arrange on a heatproof serving platter. Keep the cooked cheese warm in the oven as you deep-fry the next batch. When all are cooked, serve the cheese with a bowl of the hot pasta sauce for dipping.
Note: Bocconcini cheese is sold in bulk and in tubs. In this recipe, 2 (180-gram) tubs were used.