Finely slice the clean vegetables cross or lengthwise, using a mandoline slicer. Lightly oil a round oven-proof dish. Starting from the outside, arrange the vegetables in a dish in an upright position alternating colors. Press them in tightly. This task may need extra patience or a third hand to help. Alternatively, use a square dish or arrange vegetables in rows, or layers like lasagna. There’s no wrong way of layering.
Tuck garlic pieces between the vegetable rows. Drizzle with oil, season with salt and pepper, and top with thyme. Bake uncovered until vegetables are tender, about 50-60 minutes. Serve warm or at room temperature garnished with torn basil leaves.