Peel and finely chop the onion. Peel the carrots and the potatoes. Cut the carrots into small pieces and the potatoes into medium-sized pieces. Heat the oil in a large pot and sauté the onions and carrots. Add the potatoes and the vegetable broth.
Simmer until the vegetables are soft. Remove from heat, cool slightly and mash. Set aside and reheat. If the soup is too thick, add a little more water. Stir in the grated cheese and let it melt in the soup. Season to taste with herbs and spices.