Preheat the oven to 400 degrees F.
Put all the vegetables and the herb sprigs in a large baking dish. Season well with salt and black pepper, drizzle generously with olive oil, and toss them with your hands to coat them evenly.
Put the baking dish in the preheated oven and cook, stirring the vegetables occasionally, until they are tender and golden brown, about 45 minutes. Serve the vegetables from their baking dish or transfer them to a platter to accompany a roasted main course.