Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add potatoes, cover, and steam until tender, about 20 minutes. Drain well.
Preheat the oven to 400 degrees F (200 degrees C). Lightly grease a 13x9-inch baking dish.
Cut each potato into 2 to 3 large slices and arrange pieces at ends of the prepared baking dish. Set leeks next to potatoes, then arrange carrots, onions, red peppers, and mushrooms over and around the leeks and potatoes. Drizzle vegetables with olive oil and sprinkle with thyme, salt, and pepper.
Roast in the preheated oven, basting with pan juices every 15 minutes, until vegetables are tender when pierced with a fork, 45 to 60 minutes.