Make a bouquet garni: First wrap bay leaves, rosemary, parsley, and peppercorns in a piece of cheesecloth. Then tie with a piece of kitchen twine, and set aside.
Heat olive oil and butter in a medium stockpot. Add celery, leeks, shallots, and garlic; cook on medium-low heat until very soft, about 45 minutes, stirring only occasionally. Do not brown. Add potatoes, stock, and reserved bouquet garni. Bring mixture to a boil, and then reduce to a gentle simmer. Cook until potatoes are very tender, about 40 minutes. Remove bouquet garni, and discard.
Working in batches, pass half of the soup through a food mill, fitted with a medium disk, into a large saucepan. Add remaining chunky soup. Place the saucepan on medium-low heat to warm soup. Slowly stir in milk and cream, and season with salt and pepper. Serve hot.
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