Cook celery in ½c. water just until tender. Do not drain.
Peel and cube potatoes. Place in 4-qt. saucepan with 2 c. water. Add cooked celery, onion, salt and pepper. Cook until potatoes are tender. Mash slightly to eliminate definite cubes. Add milk; set aside until dumplings are mixed.
To make dumplings, sift together flour, baking powder, salt and sugar. Stir in parsley flakes.
Beat eggs; add milk; add to dry ingredients and mix just until moistened.
Bring soup to a boil. Drop dumplings by tablespoonfuls into liquid so they don’t touch. Turn heat to simmer, cover tightly; simmer gently 20 minutes. Don’t lift lid.