Preheat oven to 450 deg F. Line 2 baking sheets with aluminum foil.
Chop eggplant, zucchini, bell peppers and onion into 1/2" size pieces.
Place in a large bowl and drizzle with olive oil. Toss with a spatula or with your hands to coat evenly. Add more oil if vegetables look dry.
Divide the vegetables between the 2 baking sheets and spread them in a single layer. Do not overcrowd the sheets or the vegetables will not caramelize properly.
Sprinkle each sheet generously with salt and pepper.
Chop the garlic coarsely, and spread half of it over each sheet.
Place the sheets in the oven, one in the upper third, the other in the lower third. Bake for 30 minutes.
Keep an eye on the vegetables as they roast. Once or twice during the 30 minutes, take each sheet out and toss the vegetables so they don't stick to the sheet. You may also need to swap the sheets' position so they both cook evenly.
While the vegetables are roasting, cut the cherry tomatoes in half.
After 30 minutes, the vegetables should be soft and just starting to brown. Remove the pans from the oven and distribute the tomatoes, giving another toss to incorporate them with the rest of the vegetables.
Bake for another 10 minutes, until the tomatoes are soft and releasing their juices and their skins are wrinkled. The rest of the vegetables should be nicely browned and caramelized.
Remove the vegetables to a serving dish. Cut the basil into thin strips and add them to the vegetables. Taste and add salt and pepper if necessary.