In a large saucepan, bring 1 1/2 quarts of water to a boil. Add baby artichokes and cook approximately 7 to 10 minutes or until you can easily pierce them with a fork, but they still offer some resistance. Drain and immediately immerse in cold water to stop the cooking.
When cool, cut the baby artichoke in half lengthwise, sprinkle them with olive oil, and salt and pepper to taste.
Prepare the grill. Cover barbecue with lid, open any vents, and grill them over a medium-hot fire, cut side down for about 5 minutes, or until the cut sides are well browned.
Serve with any dipping sauce like garlic aioli or garlic butter.