Combine the carrots, eggplant, onion, red and yellow peppers, garlic cloves, and tomatoes in a large mixing bowl. Add 3 tablespoons olive oil, 1 teaspoon salt, 1 teaspoon pepper, and the Italian seasoning. Mix well and divide the vegetables between 2 rimmed baking sheets. Roast, stirring every 10 minutes, for 30-35 minutes, or until the vegetables are tender and starting to brown.
While the vegetables are roasting, cook the fusilli. Bring a large pot of heavily salted water to a boil. Cook the fusilli according to the package directions. Reserve about a cup of the pasta cooking water and drain.
Place the cooked fusilli in a large mixing bowl along with the vegetables, 2 tablespoons olive oil, ¾ cup Parmesan cheese, and the basil. Stir gently to combine. Add some of the reserved pasta water, a little at a time, to moisten.
Season to taste with more salt and pepper. Serve with more Parmesan on top, if desired.