Heat the butter and oil in a large pan over medium heat. Add the chopped onion, turning it until well coated. Stir in potatoes. Cover and sweat over low heat for 5-10 minutes. (until softened but not browned)
Then, add the mushrooms, garlic and white wine or cider and stock. Season to taste, bring to boil and cook for 15 minutes, (until all ingredients are tender)
Put mixture through a food mill, or blend. Return the soup to the rinsed pan and add three-quarters of the parsley. Bring back to boil, season and garnish with cream and remaining parsley.