Place the artichokes in a pot of water and bring to a boil. Simmer until the artichokes are tender. You should be able to pierce into the center of the artichoke with a fork easily. Remove and cool.
While the artichokes are cooling, in a bowl, combine the rest of the ingredients and reserve.
When cooled, cut the artichoke in half length wise and remove the hard center leaves and scrape out the hairy fiber pieces attached to the heart of the choke.
Mix the balsamic dressing and drizzle the insides of the artichoke with ¼ cup of the dressing. Marinate overnight, or at least 2 hours.
Preheat a grill and grill the artichokes to caramelize the outer sides and lightly char. Remove and place on a serving platter. Drizzle with fresh dressing and serve the extra dressing with the artichoke halves on the side.
To eat, peel away the “petals” and scrape off the meat with your teeth. As you get to the center, you will be able to eat more and more of the tender part of the “petal.”
Once you get all the way to the center of the artichoke, you can slice up the “heart” and eat, or save for a side dish.