Cook spaghetti as directed on package. Drain; rinse with hot water. Cover to keep warm; set aside. Cook vegetables until crisp-tender as directed on package. Drain; set aside.
Meanwhile, heat oven to 400°F. Grease 13x9-inch (3-quart) glass baking dish. Melt butter in medium saucepan over medium heat. Stir in flour until smooth. Gradually add milk, cooking and stirring until well blended. Cook 6 to 10 minutes or until mixture boils and thickens, stirring constantly. Stir in 1/2 cup Parmesan cheese and the pepper.
Spoon cooked spaghetti into greased baking dish. Top with cooked vegetables and sliced mushrooms. Pour milk mixture over mushrooms. Sprinkle with 2 tablespoons Parmesan cheese.
Bake at 400°F. for 15 to 20 minutes or until mixture bubbles around edges and is thoroughly heated.