Prepare the quick cook rice according to package directions.
When the rice is ready, allow it to cool and then put it in a large bowl and stir in 1 egg, ¼ cup breadcrumbs, ⅛ teaspoon salt, dash of pepper, ½ teaspoon of oregano, ¼ cup Parmesan cheese and 1 cup of shredded mozzarella cheese. Mix until thoroughly combined.
Use your hands to form into small balls.
Beat two eggs in a bowl and dip the formed rice balls in the egg. Roll the rice balls around in the bread crumbs until they are completely covered.
Place the oil in a pan so that when the arancini are added, the oil will cover or nearly cover them. Heat oil until it is 350 degrees. Using a slotted spoon, drop in balls in batches of four until they are cooked through and the outside has turned a deep golden brown.
Remove the arancini balls from the oil with a slotted spoon and place them on a plate lined with paper towels. Sprinkle with salt. If you'd like, you can warm up some marinara sauce for dipping and serve the sauce with the rice balls.