Place chicken pieces in a Dutch oven.
Add 4 cups water, celery, carrots, onions, salt, thyme, and pepper. Bring to boil.
Reduce heat, cover, and simmer 35-45 minutes or until chicken is nearly tender. Skim off fat.
Blend 1 cup water and flour together and then stir into chicken mixture.
Stir in frozen peas and mushrooms. Cook, stirring gently until thickened and bubbly.
Drop herb dumplings dough (see recipe below) by tablespoon onto stew.
Cover and simmer 15 minutes without lifting lid. Sprinkle with parsley and serve.