In a medium bowl whisk together eggs, cheese, parsley, pepper and 1 teaspoon salt. Cover and refrigerate.
Pour water and 1 teaspoon salt into a large saucepan and bring to a boil. Stir in rice and reduce heat to low. Cook rice until water is almost absorbed stirring frequently. Remove from heat and slowly pour in egg mixture; stirring rapidly to prevent egg from scrambling. Allow rice mixture to cool for 1 hour.
Pour breadcrumbs into a pile on one end of a cutting board. Dampen hands and roll rice mixture into 2cm balls then coat each one with breadcrumbs.
In a small deep frypan heat olive oil to 180 degrees C. (Should have enough oil to completely cover rice balls.) Fry rice balls 6 at a time turning as needed to ensure even browning. Drain on paper towels and serve warm.