Put the chicken stock, potatoes, leeks, celery, bay leaf and thyme in a large pot and sprinkle with salt and pepper. Boil until the potatoes are soft, 15 to 20 minutes. Remove the bay leaf. Using an immersion blender (or in batches in a blender or food processor), blend the soup until smooth. Pour the soup into a medium pot; add the cream and simmer until the soup has thickened, about 20 minutes.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.