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.
From Food Network Kitchens; after further testing and to ensure the best results this recipe has been altered from what was in the actual episode.
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.