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