Prepare charcoal fire or preheat gas grill for covered direct grilling over medium-high heat.
Meanwhile, mix in a cup, the oil, vinegar, salt, pepper and chopped basil.
Place red and yellow peppers, eggplants, and squashes on hot grill rack. Cover grill and cook vegetables until tender and browned (7 to 10 minutes), turning and brushing with herb mixture occasionally and transferring vegetables to platter as they are done.
Drizzle vegetables with any remaining herb mixture.