Preheat oven to 350°F. Remove meat from chicken; discard bones. Cut chicken pieces in chunks to equal 3 cups. Save remaining chicken for another use. In Dutch oven cook spaghetti according to package directions. Add asparagus the last minute of cooking. Drain. Return to pan.
Meanwhile, in large skillet cook mushrooms and sweet peppers in hot butter over medium heat for 8 to 10 minutes or until mushrooms are tender, stirring occasionally. Stir in flour and black pepper until well combined. Add broth and milk all at once. Cook and stir until thickened and bubbly. Add mushroom mixture, chicken pieces, Swiss cheese, and half the lemon peel to pasta mixture in Dutch oven. Toss gently to coat. Spoon pasta mixture into 3-quart rectangular baking dish. In a medium bowl toss together bread cubes, olive oil, and remaining lemon peel. Spread bread cube mixture on pasta mixture.
Bake, uncovered, for 15 minutes or until heated through. Let stand for 5 minutes before serving. Sprinkle with parsley before serving.