To make the risotto: In a medium-sized saucepan, heat the stock until almost a boil. Turn the heat to very low and stir in the saffron.
In a 10- to 12-inch saucepan, melt 3 tablespoons of the butter. Immediately stir in the rice and cook over medium-high heat. Using a wooden spoon, stir continuously until the rice is coated in the butter and begins to turn translucent, about 2 minutes. Be careful not to let the rice burn. Keeping the heat at medium-high, begin ladling the hot broth into the rice, about 2 ladlefuls at a time. Constantly stir with the wooden spoon until the rice has almost absorbed all of the broth. Continue adding the both bit by bit until the rice is al dente or tender, about 20 minutes. Once the rice is cooked, season with salt and pepper. Remove from the heat and immediately add the egg yolk and the remaining tablespoon butter. Stir to thoroughly combine and set aside to cool.
To make the ragu: in a large, heavy-bottomed saucepan, cook the olive oil, veal, and onion over high heat. Stir often, and continue cooking until the veal loses its pink color.
Add the remaining ingredients through the 3 cups of chicken stock. Turn the heat to medium low and allow the ragu to simmer for about 1 hour to 1 hour 30 minutes, until quite thickened. Season to taste with salt and pepper, stir well to combine, and remove the ragu from the heat. Let the ragu cool, about 45 minutes.
When the ragu is cool to the touch, place a scant cup of rice into the palm of one hand and use the fingers of your other hand to form a cup-like mound of rice. Place a generous tablespoon of the ragu into the rice cup, then gently fold the outer edges of the rice over to cover the ragu, completely enclosing it. You should have a ball of stuffed rice and there should not be any ragu leaking out. You may need to add a little more rice to keep close the ball. Set the arancine aside and use the remaining rice and the remaining ragu to make about 7 more balls.
Roll each finished ball carefully through the beaten egg whites, then dredge through the breadcrumbs. Place the arancine on a tray and refrigerate for 30 minutes.
In the meantime, heat 4 inches of cooking oil in fryer or deep frying pan to 375 F. When the oil has reached temperature and the arancine have had time to cool, carefully place 3 balls at a time into pan and fry until golden brown, about 3 to 4 minutes, stirring with tongs or kitchen spoon to keep them moving. Drained cooked balls on paper towels and place on large platter. Serve immediately.
Recipe courtesy of Mario Batali