Peel the onions and garlic and chop finely. Peel the carrots and celery, wash and dice. Remove the outer leaves and the green part of the leeks, wash and cut into fine rings. Heat the oil in a large pan and slowly sauté the vegetables.
Peel, wash and dice the potatoes and add. Before the vegetables turn color, add the boiling water and season with salt, pepper, thyme and the 1/2 bay leaf. Cover the pot and leave to simmer for 45 minutes. A
dd the hot milk and half the grated cheese. Leave to cook for a further 10 minutes and check the seasoning.
Serve the soup, offering the rest of the grated cheese at the table. This soup also works very well with ripe Manchego cheese.