Heat oil in deep-fryer to 375 degrees F (190 degrees C).
Sandwich the mozzarella cheese between Italian bread slices.
In a small bowl, mix the Parmesan cheese into the eggs.
Place the bread crumbs in a small bowl.
Dip both sides of the sandwich into the egg mixture, then into the bread crumbs, coating thoroughly.
Carefully place the coated sandwich into deep fryer. Cook 2 to 4 minutes, or until bread is golden brown and cheese has melted. Remove from oil, drain on paper towels and cut into 4 triangles to serve.