Steam globe artichokes in 2 cups of water until tender, about 45 minutes. Reserve the cooking liquid and set artichokes aside until cool enough to handle.

Scrape the flesh from the bottom third of each leaf and place in medium soup pot along with the artichoke liquid.

Remove fuzzy choke from each artichoke bottom and discard.

Coarsely dice the artichoke bottoms and place in the soup pot. Add chicken stock, vermouth, potato, carrot, onion, celery, garlic, bay leaves, and marjoram. Simmer until vegetables are very tender and liquid is reduced by 1/3, about 45 minutes.

Remove bay leaves and puree soup with an immersion blender until smooth.