Start a multilevel charcoal fire or preheat your gas grill to medium high. Brush all the vegetables with olive oil and sprinkle with salt and pepper. Thread vegetables, except scallions, on two parallel skewers. Place scallions directly on grate.
Grill, turning once or twice, until nicely browned on both sides and tender throughout, about 15 minutes (delicate vegetables, such as the scallions, will finish sooner; set aside). Drizzle with a little more olive oil, garnish, and serve hot or at room temperature.