Heat oven to 400°F. Spray 13x9-inch (3-quart) glass baking dish with cooking spray.
Cook and drain fettuccine as directed on package. Meanwhile, in 12-inch nonstick skillet, heat oil over medium-high heat. Cook mushrooms, onion, thyme, salt and pepper in oil 10 minutes, stirring occasionally, until tender. Remove from heat. Stir in flour; gradually stir in broth. Heat to boiling; boil 1 minute. Remove from heat; stir in whipping cream.
Add cooked fettuccine and parsley to skillet; toss. Add goat cheese; toss gently. Spoon into baking dish.
Cover; bake 15 minutes. Uncover; sprinkle with Parmesan cheese. Bake 10 to 15 minutes longer or until thoroughly heated and bubbly.