Place a large heavy-bottomed pot over medium heat and add enough vegetable oil to rise 4 inches in the pot.
Combine the rice, Parmesan and 1 egg in a medium bowl and use your hands to thoroughly combine the mixture.
Form each arancini by taking a small portion of the mixture, squeezing it firmly and stuffing one cube of mozzarella inside each ball.
Repeat this process to form 8 arancini.
Whisk together the remaining 2 eggs. Dip each arancini in the eggs and then in the breadcrumbs, shaking off any excess.
Once the oil reaches 375ºF, add 2 or 3 of the breaded arancini to the pot and fry them until golden brown and cooked throughout.
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.
Serve the arancini warm with a side of warm marinara sauce.
I've made arancini with many types of rice, but some varieties prove more successful than others. For example, regular old Uncle Ben's will only work if it's particularly sticky. The best rice for arancini is actually sushi rice (despite how unauthentically Italian that may be!) because it is much more glutinous so it's easy to work with.
Make sure you really squeeze the arancini together to make them as compact as possible. This will ensure the arancini hold their shape when frying.