Heat the oil in a dutch oven over medium heat. Add the potatoes, leeks, shallots, celery and thyme. Salt and pepper. Cook 10 minutes stirring every few minutes. Add the white wine and deglaze the bottom of the pan. Add the chicken stock and cook until the potatoes are tender. (about a half hour) Transfer everything to a food processor and blend until smooth. Add the mixture back to the pan and add the cream to it. Heat through. Salt and pepper to taste. Serve with the parmesan cheese on top.
Fried bacon crumbles and sour cream also make a great garnish for this soup.