Bring 3/4 l of salted water to a boil. Peel, wash and slice the carrots. Clean the leek and cut into rings.
Peel and dice the onion. Add the rice to the boiling salted water and let it swell over low heat for about 20 minutes. Heat the oil in a pot and fry the onions in it. Add the vegetables, 1 1/4 l of water, and the grained broth and bring to a boil. Cover and cook for 15-20 minutes.
Slice the sausages and heat them in the soup just before the end of the cooking time. Wash the parsley and cut into fine strips. Drain the rice and add to the soup.
Season with salt, pepper and nutmeg and serve sprinkled with parsley.
