Heat the olive oil in a saucepan over a low heat. Add the carrot, celery and shallot and cook for 8–10 minutes until soft and translucent. Add the minced beef and cook, stirring and breaking up with a wooden spoon, for 5 minutes until lightly golden. Stir in the tomatoes and tomato purée. Bring to the boil, then reduce the heat and simmer very gently for about 30 minutes until the sauce becomes very thick. Leave to cool, then cover and chill for at least 1 hour.
Wet your hands, take 1 tablespoon of the cooked risotto and flatten slightly. Mould around 1 teaspoon of the meat filling to form a ball, making sure that the filling is completely encased. Repeat with the remaining risotto and filling.
Roll each arancino in the flour, then dip in the beaten egg and roll in the breadcrumbs to coat.
Heat enough sunflower oil for deep-frying in a deep saucepan to 180–190°C (350–375°F), or until a cube of bread browns in 30 seconds. Add the arancini to the hot oil, in batches, and cook for about 3–4 minutes until golden all over. Remove with a slotted spoon and drain on kitchen paper. Serve immediately.