Put the fresh parsley, the garlic, bay leaves, lemons, wine, oil, and broth in a large pot. Bring to a simmer and season with salt and pepper.
Wash the artichokes under cold water and cut the stems off close to the base of the artichoke. Pull off the lower, tough leaves around the stem. Cut off the top inch of the artichoke and rub with lemon. The thorny tips of the leaves may be trimmed with scissors, if desired.
Place the artichokes in the simmering broth, bottom side up. Cover and simmer for about 30 minutes or so. They will be done when you can easily insert a knife into the base.