Cook pasta according to package directions, omitting salt and fat; drain. Place in a large bowl. Add 2 teaspoons olive oil, basil, oregano, 1/2 teaspoon salt, and 1/2 teaspoon pepper to hot pasta, and toss well to combine.
Heat remaining 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add tomatoes and garlic; sauté 2 minutes. Add chives and thyme; sauté 1 additional minute or until tomatoes are slightly charred and skins are just beginning to burst. Add broth; bring to a boil. Cook over high heat 1 minute. Add tomato mixture and parsley to pasta; toss gently to combine. Sprinkle with cheese; serve immediately.