Put the beef into a bowl and knead with dampened hands for a few minutes until soft. Add the onion, half the parsley and the beaten egg. Mix together with a wooden spoon, stir in the mushrooms and season with some salt and plenty of pepper. Form the mixture into ping-pong sized balls.
Heat the olive oil in a large frying pan and fry the balls over a high heat for a few minutes, just to brown them, turning carefully once or twice. Remove from the heat.
To make the sauce, make a small incision in the tomatoes and place in a bowl. Cover with boiling water and leave for a minute. Drain, remove and discard the skin and finely chop the flesh. Heat the butter in a large, heavy saucepan and add the chopped tomatoes, onion and garlic. Cover the pan and leave to simmer gently for 8–10 minutes, or until the tomatoes are very soft and mushy. Stir in the sugar and season to taste with salt and pepper.
Spoon the rissoles into the tomato sauce together with any juices from the pan. Cover and simmer very gently for 20 minutes. Sprinkle with the remaining parsley and serve straight from the pan.