1. In a mixing bowl, combine the cooked rice, Parmesan cheese, and one beaten egg.
2. Take a small amount of the rice mixture and flatten it in your hand. Place a cube of mozzarella in the center and shape the rice around it to form a ball.
3. Roll the ball in flour, then dip it in the remaining beaten egg, and finally coat it with breadcrumbs.
4. Heat the vegetable oil in a frying pan over medium heat. Fry the rice balls until golden brown, about 3-4 minutes per side.
5. Remove the arancini with a slotted spoon and drain on paper towels. Serve hot.