In order to grill artichokes, you have to steam them first. Table talk: We tested a fancy steaming mixture that had about 10 ingredients, including wine, but found this simple mixture that calls for lemon and garlic imparts great flavor for a lower cost.
Combine lemon, next 3 ingredients, and 2 1/2 cups water in large Dutch oven. Place a steamer basket in Dutch oven.
Wash artichokes by plunging up and down in cold water. Cut off stem ends, and trim about 1 inch from top of each artichoke, using a serrated knife. Remove any loose bottom leaves. Trim one-fourth off top from each outer leaf, using kitchen shears.
Arrange artichokes in steamer basket. Bring to a boil; cover, reduce heat, and simmer 35 to 40 minutes or until stem end is easily pierced with a long wooden pick. Remove artichokes from Dutch oven. Let cool 15 minutes.
Preheat grill to 350° to 400° (medium-high). Carefully cut artichokes in half lengthwise; remove and discard choke. Liberally brush cut sides of artichokes with olive oil, and sprinkle with desired amount of salt and pepper.
Grill artichokes, covered with grill lid, over 350° to 400° (medium-high) heat 5 minutes on each side. Serve with Buttery Dipping Sauces or Mayo Mixtures. Garnish, if desired.
Steamed Fresh Artichokes: Prepare recipe as directed through Step (Do not cool.) Carefully pull open center leaves of artichokes. Remove and discard choke using a long spoon. Serve with Buttery Dipping Sauces or Mayo Mixtures. Makes 4 servings; Prep: 15 min., Cook: 45 min.