Cook pasta according to package directions, omitting salt and fat. Drain. Place in a large bowl.
While pasta cooks, combine basil, onions, minced garlic, and tomatoes in a food processor. Pulse 10 times or until coarsely chopped. Add Parmesan to pasta, stirring until cheese melts. Stir in tomato mixture, olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper; toss gently to coat pasta. Top with mozzarella.