Preheat oven to 400°F. Lightly oil a large, shallow roasting pan. As you cut up each of the vegetables, transfer to the pan.
When all of the vegetables and the garlic are in the pan, drizzle with olive oil and vinegar. Season with salt and black pepper. Toss to coat everything with oil and mix in the basil. Roast, uncovered, for 50 to 60 minutes, stirring two or three times during the last half of cooking. When done, some vegetables will be tender, some crisp, and there will be very little juice in the bottom of the pan. Serve hot.