Prepare the herbed oil: Cut garlic head in half crosswise; remove as many dried skins from garlic as you can. Place olive oil and garlic halves in a small saucepan over low, and bring to a simmer. Cook until garlic is golden brown, about 30 minutes.
Remove oil from heat; cool 20 minutes. Pour through a fine wire-mesh strainer into a blender; discard solids. Add parsley, basil, salt, and crushed pepper; process until herbs are finely pureed and oil takes on a green hue. Chill until ready to grill lobsters.
Prepare the lobsters: Light charcoal briquettes in a large grill, and allow fire to burn until coals are gray and very hot (high heat, 450°F to 500°F).
Fill a large pot with 3 gallons cold water. Add white wine, vinegar, and salt to water; cover and bring to a rolling boil over high. Add lobsters, and cook 3 minutes.
Remove lobsters with tongs, and cool 10 minutes. Split whole lobsters lengthwise down the middle with a long, sharp knife. (Do your best to split cleanly, to keep as much of the tomalley and roe intact inside the lobster shell.) Brush meat side of each lobster with 2 teaspoons of the herbed oil.
Place lobsters on oiled grill rack, meat side down. Grill lobsters, uncovered, until starting to char, 2 to 3 minutes. Carefully flip them over, and grill until bubbles start to form around the meat, about 2 minutes. Remove from grill. Serve with lemon wedges, and drizzle with herbed oil.
Providence, Los Angeles