Bring the 6 cups of water to boil in a large pot
Stir in rice and salt, lower the temperature slightly, cook until rice is tender and soaks up all or most of the water; about 20 minutes
Drain rice if needed, spread out on a cooking sheet to cool the rice
In a large sauce pan add the olive oil, saute the diced onions and carrots until golden – add more olive oil if needed to cover the onions and carrots
Brown the ground beef with the onions and carrots
Add the tomato sauce, ½ to 1 TBS salt (to taste), 1 tsp of pepper (to taste), and sugar
Simmer until thicken, about 20 to 30 minutes – the sauce needs to not be runny because it will be placed inside the rice balls
Add the green peas and let simmer an additional 5 minutes
Remove sauce from heat and let cool to touch
In a small bowl, whisk the 2 eggs until completely combined
In another small bowl add the fine breadcrumbs
Wet your hands in the bowl of water to prevent rice from sticking
Take about ¼ cup of rice and spread over your hand to make a layer of rice sticky together
Scoop about 2 TBS of ragu – tomato sauce and ground beef – in the middle of the rice
Work the rice into a ball to surround the ragu, make sure there are no openings – they should be about 2 inches in diameter
Continue to form all the stuffed rice balls, wetting hands slightly between each rice ball as needed
Dip a rice ball in the egg, swirling around to cover
Dip the rice ball in the breadcrumbs and cover completely with breadcrumbs, place on another cooking sheet
Repeat until all stuffed rice balls are covered with breadcrumbs
In a wide diameter pot, add the vegetable oil – you want to be able to fry 3 to 4 rice balls at a time
Once the oil is to a temperature ready for frying, place 3 to 4 rice balls into the oil
Let fry for a minute or two until golden brown, turning to brown all sides
Remove using a slotted spoon or spatula and lay on paper towel to drain
Continue until all arancini are fried