Cook the rice according to the instructions on the package. Once cooked drain any excess water if needed, season with salt and pepper. Then lay out in a thin layer on a plate or baking sheet to cool, about 10 minutes.
Mix the rice and parmesan. Equally portion and form the rice into a balls around the cube of mozzarella (dampen your hands with water beforehand to prevent the rice from sticking).
Heat the oil in a saucepan or sauté pan over medium heat to 350°F.
Dip each arancini into the egg and then into the breadcrumbs, pressing and forming with your hands to coat well.
Once the oil is hot, add the arancini to the pot and fry them until golden brown, turning as needed. Work in batches if needed so as to not overcrowd the oil.
Use a slotted spoon to remove the fried arancini from the pot and transfer them to a paper towel-lined plate. Immediately salt the arancini. Repeat the frying process with the remaining arancini.