Cook noodles according to package directions; drain. Return to hot pan; cover and keep warm.
Meanwhile, in a 4- to 5-quart Dutch oven heat oil over medium heat. Add onion, carrot, and celery; cook for 5 minutes, stirring occasionally. Sprinkle with flour, thyme, and poultry seasoning; cook and stir for 1 minute more. Stir in broth, potato, the water, and salt.
Bring to boiling; reduce heat. Simmer, covered, for 20 to 25 minutes or until potato is tender. Using a potato masher, coarsely mash about half of the potato. Stir in chicken, peas, and evaporated milk; heat through. Stir in cooked noodles. If desired, sprinkle each serving with pepper.