Preheat oven to 375°.
Combine first 5 ingredients in a shallow roasting pan, and toss well. Sprinkle with salt, rosemary, and pepper. Bake at 375° for 25 minutes or until onion is tender, stirring occasionally. Squeeze garlic cloves to extract pulp; discard skins. Place garlic pulp, onion, tomatoes, and chicken broth in a food processor; process until well blended.
Combine mushrooms, tomato mixture, pasta, parsley, and chives in a large bowl, tossing well. Sprinkle with cheese.