I am a grilling fool. One with a marked propensity or fondness for something, not a simpleton. Anyway, I love my grill pan and researched a bit about how to grill baby artichokes. Cut them in half and boil them in water along with rosemary and garlic cloves for about 5 minutes. Drain and brush them with olive oil, salt and pepper. Grill them about 5 minutes a side. When they're done give them a squeeze of fresh lemon juice on the cut side and enjoy!.