Make the stuffing: Combine the olive oil, meat, carrot, celery, and onion in a medium saucepan and cook over medium-high heat until browned. Stir in the tomato sauce and estratto, reduce the heat to low, and cook until thickened, about 30 minutes. Season with salt and pepper to taste. Remove from the heat and set aside to cool.

Meanwhile, make the rice: Combine the olive oil and onion in a medium sauce­pan and cook over medium heat until softened, about 5 minutes. Add the rice and stir to coat with oil. Add the water and as soon as it comes to a boil, stir in the saffron, then cover, and remove from the heat. Let stand for 15 to 20 minutes, until the water is absorbed and the rice is tender. Stir in the Parmesan and salt and pepper to taste, then spread out onto a large plate to cool.

Make the batter: Whisk together the flour, water, and eggs in a large shallow bowl until the batter is smooth and creamy. Fill another shallow bowl with the breadcrumbs. Put a bowl of cold water next to you, to wet your hands now and then; this will help the rice stick together.

To assemble the rice balls, wet your hands in the cold water and fill the palm of one hand with a spoonful of rice. Cup your hand and make a hole in the middle, pushing the rice to the same thickness all around. Fill the hole with 1 small spoonful of stuffing and close your hand, enclosing the meat sauce with the rice. (Add more rice if you need to round out the ball,) Keep the hand with which you are spreading the rice wet. The ball should to be no bigger than a very small orange, from which it takes its name.

As you make them, roll the arancine in the batter to coat, compacting them with your hands. Then roll them in the breadcrumbs and coat; again pat them thoroughly with your hands. Place on a baking sheet that is sprinkled with breadcrumbs.

Heat 2 inches of vegetable oil in a large heavy skillet. Add the arancine in batches and fry, turning occasionally, until crisp and golden, 3 to 4 minutes. Drain on paper towels and serve warm.