Combine chicken, 1 clove garlic, half the wine, half the basil (or 2 tsp. Lemon juice) in bag and refrigerate 2 hours or overnight. Steam asparagus until just tender, then refresh under cold running water and set aside.
Saute morels in 1 Tbs. butter until tender, add wine, garlic and herbs, then set aside. Stir fry chicken and add morels, asparagus and chicken broth. Thicken with cornstarch if needed.
Drain the noodles and melt 2 Tbs. butter in large saucepan. Toss noodles in butter over medium heat and add the milk. Cook and stir until milk is absorbed. Add cheese and toss, then vegetables and chicken. Stir together and serve immediately. Top with additional cheese if desired.