Adjust oven rack to middle position. Heat oven to 475°F.
Heat olive oil in a 12-inch, oven-safe skillet over medium-high heat. Add the mushrooms, zucchini, bell pepper, and onion; sauté until the onion is translucent and the other vegetables start to soften, about 5-7 minutes. Add the garlic, red pepper flakes, and ½ teaspoon salt; cook for 1 more minute.
Add the crushed tomatoes, water, ziti, sugar, and ½ teaspoon salt. Cook, uncovered, stirring often and adjusting the heat as necessary to keep the liquid at a good simmer, until the ziti is almost tender, about 15-18 minutes. Add extra water, if necessary, if the sauce looks too thick.
Stir in the cream, the grated Parmesan cheese, and the minced fresh basil. Season the dish with additional salt and pepper to taste.
Sprinkle the Italian cheese blend evenly over the top of the pasta.
Transfer the skillet to the oven. Bake, uncovered, until the cheese melts and browns on top, about 10 minutes.
Garnish with additional fresh basil just before serving.