Preheat the oven to 400°F. Adjust the rack to the center of the oven. Spray a sheet pan with oil.
Place the vegetables in a bowl and drizzle with olive oil, garlic, salt, black pepper, breadcrumbs and half of the parmesan cheese and toss well to coat.
Spread out onto a sheet pan and roast in the center of the oven until the vegetables are tender-crisp and browned on the edges, tossing halfway, about 20 to 30 minutes.
When vegetables are cooked and browned on the edges, remove from oven and top with remaining grated cheese. Serve hot.