My mother makes these on the Monday after a big Sunday sauce, using whatever ragù is left over rather than making a fresh batch -- which is not a shortcut, in this case, but the actual, correct way to do it. A ragù that has had a day to sit in the refrigerator is better for this than one made the same day, thicker and more concentrated, exactly what a filling like this wants.
Makes about 10 arancini.
Cook the rice in salted water with the saffron until tender, then drain well -- you want it dry, not soupy, since wet rice will never hold together around a filling. While still warm, stir in the butter and Parmigiano, then spread it out on a low tray and let it cool completely, at least two hours. This is not a step to rush. Warm rice will not hold a shape.
Wet your hands, and take a generous handful of the cooled rice -- about the size of a small orange. Flatten it in your palm, and press a small well into the center. Spoon in a little of the cold ragù and two or three cubes of mozzarella, then cover with a little more rice, and gently work the whole thing into a compact ball, sealing the filling completely inside. Any gap left open is where the oil will find its way in later.
Roll each ball in flour, then in the beaten egg, then in breadcrumbs, pressing gently so the coating holds. Let them rest for ten minutes before frying -- this settles the coating and reduces the chance of it cracking in the oil.
Heat the oil to 175°C (350°F), and fry the arancini a few at a time, turning them so they color evenly, until deeply golden all over, about four to five minutes. Drain on paper towels, and let them sit for a few minutes before eating -- the filling holds real heat, more than the crust suggests from the outside.
If the arancini fall apart in the oil, the rice was not cooled and dried enough before shaping, or the filling was not fully sealed inside; a gap in the rice is a door the oil will walk straight through. If the outside browns before the inside is properly hot, your oil was too hot to begin with; bring it down closer to 175°C and give the frying more time rather than more heat. And if the filling tastes thin and watery instead of rich, your ragù was too fresh -- this is genuinely one dish where a sauce that has sat in the refrigerator overnight outperforms one made the same day.