In a pot with thick bottom heat oil with butter, add peeled and diced potatoes and fry them for about 5 minutes, stirring occasionally.
Pour in hot broth and bring to a boil. Reduce heat and cook for about 20 minutes covered. Trim green beans at the ends, cut into pieces and add to the soup, cook for about 15 minutes covered or partially covered. At the end the potatoes should start to fall apart.
Place sour cream in a cup and thin it with a few tablespoons of soup (to temper it), gradually add to the rest of the soup in the pot while stirring vigorously.
Sprinkle with chives or dill. Serve with smoked salmon or crumbled feta cheese.