In a medium mixing bowl combine the olive oil, garlic, rosemary or basil, and the salt. Let mixture stand for 2 hours.
Add the vegetables to oil mixture, tossing to coat. Spoon vegetable mixture onto a 24x12-inch piece of heavy foil. Bring opposite edges of foil together; seal tightly with a double fold. Fold in remaining ends to completely enclose vegetables, leaving a little space for steam to build.
Grill the vegetable packet on a grill rack directly over medium-hot coals about 20 minutes or till vegetables are tender, turning the packet over halfway through the cooking time. (Or, bake vegetables in a 350 degree F. oven ab