Put the water, chicken pieces, minced onions, chopped celery, salt, nutmeg, and black pepper into a large stockpot. Bring to a boil over medium heat, then lower to a gentle simmer and cook until the chicken is very tender, about 2 hours, adding water as needed to keep the pieces covered.

Using a slotted spoon, transfer the chicken to a deep dish. Pour the broth into a large container or jug. Cover both the chicken and the broth and refrigerate for 6 to 8 hours to let the flavors settle and the fat solidify on top.

Skim off and discard the hardened fat from the surface of the chilled broth. Return the defatted broth to a large pot over medium heat, add the corn kernels, and bring to a boil. Reduce heat and simmer until the corn is tender, about 10 to 15 minutes.

Place two of the eggs in a small saucepan and cover with cold water. Bring to a boil, then remove from the heat, cover, and let stand 10 to 12 minutes. Cool, peel, and chop the eggs finely.

Remove the chilled chicken meat from the bones and chop it into small pieces. Stir the chopped chicken into the simmering soup.

Beat the remaining egg in a medium bowl until light in color. Whisk in the sifted flour and milk until you have a smooth, thick batter. Drop tiny, pea-sized rivel dumplings into the boiling soup a few at a time, stirring as you add them.

Cook the dumplings, stirring gently, until they hold their shape and float to the surface, about 2 to 5 minutes. Stir in the chopped hard-cooked egg, adjust seasoning if needed, and serve hot.