Rub the potatoes with olive oil, salt and pepper and place on a baking sheet. Bake until tender, about 1 hour. Remove from the oven and allow to sit until cool enough to handle, but still warm
While the potatoes are baking, melt butter in a large soup pot. Add the Andouille and cook until brown. Remove from the pan, set aside. Add the onion and garlic to the pan and cook until the onions are soft, about 3 mins. Remove from heat
Peel 3 of the potatoes, add to the pot and mash until nearly smooth. Gradually stir in chicken broth and cream until blended. Return to the heat and cook until hot, stirring occasionally
Cut the remaining potatoes (with skin) in ½-inch pieces and stir into the soup. Stir in the Andouille and parsley and continue to cook until heated through. Season to taste with salt and pepper. Serve garnished with the cheese, sour cream and chives