Preheat grill to medium.
In a large bowl, toss the vegetables with olive oil and season with salt and pepper. Grill the vegetables, turning occasionally, until charred and tender, about 5 to 7 minutes. Remove to a platter. Sprinkle with basil and feta.
In a small bowl, mix garlic, balsamic vinegar, and olive oil. Season with salt and pepper and drizzle over vegetables.