In a bowl, put the mince meat along with the small finely chopped (grated) onion, the rice, salt, pepper and the egg(s) if the meat is extra lean. Mix all thoroughly and make small bite-size meatballs. Place them on a big plate or a chopping board.
Put the soup water in a pot and bring to boil.
Meanwhile, chop all the washed vegetables into small cubes or bigger chunks if you prefer. Place them all in a large bowl and set aside.
When the water is beginning to boil, put the heat down to medium and gently drop all the meatballs (one by one) with the help of a spoon. Let them cook for a few minutes until some foam will gather on the water surface. Remove this foam carefully with a spoon.
Add all the chopped vegetables to the soup and let it cook for about 10 mins.
Add some salt, tomato paste and the chopped tomatoes and allow to cook (uncovered) on medium heat until it starts boiling when you could reduce the heat to low and cook for a further 20 mins.
Put salt and pepper to taste.
Place the soup in serving bowls, sprinkle a good pinch of chopped parsley and serve.