Preheat oven to 425 degrees F. If desired, break mafalda into bite-size pieces. In a large saucepan cook pasta according to package directions, adding the broccoli and carrot during the last minute of cooking time; drain well. Place in an ungreased 3-quart rectangular baking dish; stir in tomatoes. Set aside.
Meanwhile, in a large saucepan cook mushrooms, onion, and garlic in hot oil over medium heat until liquid from mushrooms is almost all evaporated. Carefully add cream; bring to boiling. Boil gently, uncovered, for 2 minutes. Remove from heat. Stir in Asiago cheese, 1 cup of the Fontina cheese, the salt, black pepper, and crushed red pepper.
Pour cheese mixture over pasta in baking dish; stir to coat. Sprinkle with the remaining 1/2 cup Fontina cheese. Bake for 20 to 25 minutes or until sauce is bubbly. Let stand for 5 minutes. If desired, sprinkle with parsley.