In a large, heavy stockpot, melt the butter. Add the onions and cook over moderate heat until softened but not browned, about 5 minutes. Add the turnips and potatoes and stir to coat with the butter. Add salt, cover and cook over low heat, stirring occasionally, until tender, about 20 minutes.

Stir in the chicken stock and bring to a simmer. Cover partially and cook over moderate heat until the vegetables are very tender, about 10 minutes.

Working in batches, puree the soup in a blender until perfectly smooth. Return the soup to the pot and season with more salt and the nutmeg. Ladle the soup into shallow bowls and garnish with the basil or parsley before serving.