Preheat the oven to 350°. Coat a 9-inch baking dish with olive oil. Spread the potatoes in the dish in an even layer; drizzle with oil and season with salt and pepper. In a bowl, combine the bell pepper, onion, garlic and thyme and season with salt and pepper. Arrange two-thirds of the bell pepper mixture over the potatoes and drizzle with oil. Top with the tomatoes and the zucchini; drizzle with oil and season with salt and pepper. Cover with the remaining bell pepper mixture and sprinkle with the cheese.
Cover the casserole with foil and bake for 40 minutes. Increase the oven temperature to 425°. Uncover the casserole and bake for about 20 minutes longer, until the vegetables are tender and glazed on top. Let stand for 10 minutes. Serve warm.