Toss the potato, yam, bell pepper, carrots, and 2 tablespoons of olive oil in a 13 by 9 by 2-inch baking dish to coat. Sprinkle with salt and pepper and toss until coated. Spread vegetables evenly over the bottom of the pan.
Arrange the onion slices evenly over the vegetable mixture. Arrange the zucchini over the onion. Drizzle with 2 tablespoons of oil. Sprinkle with salt and pepper. Arrange the tomato slices over the zucchini.
Bake uncovered until the vegetables are tender, and the topping is golden brown, about 40 minutes. Garnish with fresh basil sprigs, if desired.