In a large saucepan, combine the chicken, broth, onion, celery, salt, thyme and pepper. Bring to a boil. Reduce heat; cover and simmer for 15 minutes or until a thermometer reaches 170°. Combine flour and water until smooth. Stir into broth. Bring to a boil; cook and stir for 1 minute or until thickened.
For dumplings, in a large bowl, combine the flour, baking powder and salt; cut in shortening until mixture resembles coarse crumbs. Stir in the milk, carrot and parsley.
Drop by rounded tablespoonfuls onto simmering broth. Cover and simmer for 20 minutes or until a toothpick inserted in a dumpling comes out clean (do not lift the cover while simmering).