Melt the butter. Add the onions and carrots, and cook them, covered, for 10 minutes or until tender. Add the stock and rice, 3/4 teaspoon of salt and freshly ground pepper to taste. Bring the liquid to a boil, and simmer for 25 minutes longer or until rice is tender as well. Remove from heat, puree in a food mill, blender or processor.
Return the soup to a saucepan and thin with water of too thick. Bring back to a boil and adjust the seasoning. Stir in cream and remove from heat or, remove the soup from heat and whisk in yogurt. Garnish with parsley