The chicken, vegetables and gravy are as rib-stickingly good as you remember, or maybe even better, tucked up cozily under a blanket of dill Havarti.
Preheat oven to 350°. Sprinkle chicken with 1/2 teaspoon salt and 1/4 teaspoon pepper. Fill a medium saucepan with water; add thyme sprig and bring to boiling. Add chicken, reduce heat and simmer, covered, for 15 to 18 minutes or until cooked through. Transfer to cutting board to cool; discard cooking liquid.
Meanwhile, melt 1 tablespoon butter in a large saucepan. Add mushrooms and onions. Cook and stir for 3 minutes or until just tender. Transfer to a bowl; set aside.
Reduce heat to medium-low. Melt remaining 4 tablespoons butter in same saucepan. Stir in flour until well combined. Stir in chicken broth, half-and-half, 1 tablespoon thyme, and remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Bring to boiling; reduce heat. Cook and stir until thickened. Set aside 1 cup sauce.
Stir carrots, celery and peas into sauce in saucepan. Cook, covered, for 8 minutes or until tender, stirring occasionally.
Chop chicken; add to sauce, along with the mushroom mixture. Simmer 2 to 3 minutes more or until heated through.
To assemble: Spread 1/3 cup of the reserved sauce in a greased 2-quart square baking dish. Top with three noodles, half the chicken mixture and a third of the cheese. Repeat layers, ending with remaining 2/3 cup sauce. (Set aside the remaining third of the cheese.)
Bake, covered, for 40 minutes. Uncover and sprinkle with remaining cheese. Bake for 5 to 10 minutes more or until noodles are tender and cheese is melted. Let stand for 15 minutes before serving.
As a shortcut, you can sub 3 cups of chopped rotisserie chicken; skip step 1 and reduce the salt in Step 3 to 1/4 teaspoon.