Make the ragu (up to 3 days in advance): heat ¼ cup olive oil in a 3-quart saucepan over medium heat. Crumble in the meet and add the onion. Cook, stirring often, until the water given off by the meat is evaporated and the meat add onion begin to brown, about 20, minutes.

Season the beef and onion lightly with the salt. Stir in the carrots and celery and continue cooking until the vegetables are tender, about 10 minutes. Stir in the tomatoes, tomato paste, red pepper, and salt to taste. Adjust the heat to simmering and continue cooking, stirring occasionally, until the sauce is thickened, about 30 minutes. If the sauce starts sticking to the pan at any time during cooking, stir in a few tablespoons of water. Stir in the peas and cook until they are tender, about 10 minutes for frozen peas and 20 minutes for fresh peas. The finished ragu should be dense and reduced. Remove and cool to Room temperature.
While the ragu is cooling, make the rice. Bring the stock or water and 2 tablespoons olive oil to a boil in a 3-quart saucepan. Stir in the rice, return the water to a boil, then adjust the heat to simmering. Cook the rice uncovered, until al dente, about 12 minutes. Drain the rice and spread out on a tray to cool to room temperature. When the rice is cool, scrape it into a mixing bowl and beat in the 4 eggs and the grated cheese.

Take a handful of the cooled rice mixture and shape it into a small ball in the palm of your hand. Make a well in the center of the ball and drop in 1 tablespoon of the ragu. Work the rice so that it completely encloses the ragu, and re-form the rice into a smooth ball. Continue forming arancine with the remaining rice and ragu.

Whisk the 2 eggs in a mixing bowl. Spread the flour on one plate and the bread crumbs on another, in an even layer.

Dredge a few of the rice balls in the flour to coat all sides. Tap off excess flour. Roll the rice balls in the beaten egg to coat, allowing any excess egg to drip back into the bowl. Finally, roll the rice balls in the bread crumbs, pressing lightly to coat evenly with the crumbs.. Remove to a clean baking sheet. Repeat with the remaining rice balls.

If you’d like to serve the rice balls, heat the oven to 200 degrees F or to the lowest setting. Line a baking sheet with a double thickness of paper towels. Pour the vegetable oil and olive oil into a deep skillet. Insert a deep-frying thermometer into the oil and heat the oil over medium heat to 375 degrees F.

Test the temperature of the oil by dipping a rice ball in. It should give off a lively but steady sizzle. If nothing happen the oil isn’t hot enough. If the oil around the bread-crumb coating boils and sputters, the oil is too hot. Adjust accordingly.

When the oil comes to temperature, carefully slip about a third of the rice balls into the oil. Fry, turning as necessary with tongues or a slotted spoon, until golden brown and crisp on all sides, about 4 minutes. Remove to the paper towel lines baking sheet, keeping them hot in the oven if you like. Fry the remaining balls. The arancine can be served hot or at room temperature.