In a steamer or in a colander over boiling water, steam artichokes 45 minutes, until tender.
While artichokes are steaming, heat butter in a large pot over medium heat. Saute leeks in butter until translucent. Remove from heat.
Scrape the flesh from each artichoke leaf and place in the pan with the leeks. Scrape the prickly choke away from the heart of the artichokes, chop the hearts and add to the leek mixture. Return to medium heat and stir to combine. Pour in broth and heat through. Slowly stir in milk, but do not boil. Season with salt and pepper. Serve hot.
