Make the Ragu up to 3 days in advance. Heat 1/4 cup olive oil in 3 quart sauce pan over medium heat. Crumble the meat and add the onions. Cook stirring often, until the water given off is evaporated and the meat and onion begin to brown, about 10 minute.
Season the meat and onion lightly with salt. Stir in the carrots and celery and continue cooking until vegetables are tender, about 10 minutes. Stir in the tomatoes, the 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 begins sticking to the pan at any time add a few tablespoons of water. Stir in the peas and cook until tender, about 10 minutes. 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 and 2 tablespoons olive oil to a boil in a 3 quart sauce pan. Stir in the rice and return to the boil, then adjust heat to a simmer. Cook the rice uncovered until tender but firm about 12 minutes. Drain the rice and spread out on a tray to cool to room temperature. When rice is cool scrape into a mixing bowl and beat in the four eggs and the grated Parmesan cheese.
Take a handful, about 1/3 cup of the cooled mixture and shape into a ball in the palm of your hand. Make a well in the center of the ball and drop in 1 tablespoon of ragu. Work the rice ball until it is completely encloses the ragu, and reform the rice into a firm 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 the other, in an even layer.
Dredge a few of the rice balls in flour to coat all sides. Tap off excess flour . Roll the rice balls in the beaten egg to coat, allowing any excess 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 would like to serve the balls hot, heat the oven to 200°F or to the lowest setting. Line a baking sheet with a double thickness of paper towels. Pour the vegetable oil and the olive oil into a deep skillet. Insert a deep frying thermometer and heat the oil to 375°F If working without a thermometer the oil around the rice ball must simmer and give a steady sizzle. Don't cook too hot, adjust heat as needed.
When the oil comes to temperature, carefully slip about 1/3 of the rice balls into the oil. Fry turning with tongs and slotted spoons until golden brown and crisp on all sides, about 4 minutes. Remove to the paper towel lined baking sheet and keep warm in oven. Fry the remaining balls. The arancine can be served warm or at room temperature.