Make bouquet garni: Wrap bay leaf, parsley, and peppercorns in cheesecloth. Tie with twine, and set aside.
Heat butter and oil in saucepan. Add leeks and shallots; cook on medium-low heat until very soft, about 10 minutes, stirring occasionally. Do not brown. Add potatoes, stock, and bouquet garni. Bring to a boil; reduce to gentle simmer. Cook until potatoes are very tender, about 40 minutes. Discard bouquet garni.
Working in batches, pass soup through food mill with a medium disk into saucepan. Warm over medium-low heat. Slowly stir in milk and cream; season with salt and pepper. Once milk is added, do not boil. Spoon into small cups; serve hot or cold, garnished with chervil leaves.