Note that the ingredients here are something of a hodgepodge: potato and sweet potato, zucchini and carrot, onion and bell pepper. That’s because this is a pretty loose recipe, and you should feel free to substitute whatever you prefer. Just be sure to cut any vegetables to roughly the same size, to ensure that they’re all fully cooked—but not overcooked—at the same time.
Preheat the Oven to 450 degrees F. In a 13x9x2-inch glass baking dish, toss the potato, sweet potato, carrots, bell pepper, 2 tablespoons of the oil, ¾ teaspoon of pepper, and ½ teaspoon of salt. Arrange the onion evenly on top, then top with the zucchini. Drizzle with 1 tablespoon of the oil and sprinkle with ½ teaspoon each of salt and pepper. Arrange the tomato slices over the zucchini. Drizzle with the remaining 1 tablespoon of oil and sprinkle with the remaining ½ teaspoon each of salt and pepper.
In a small bowl, stir the Parmesan and bread crumbs to blend and sprinkle over the vegetables. Bake uncovered until the vegetables are tender and the topping is golden brown, about 40 minutes. Let cool for 10 minutes. Garnish with fresh basil sprigs and serve.