Bring water, chicken, onions, celery, salt, nutmeg, and pepper to a boil in a large stockpot over medium heat. Reduce heat and simmer, adding water if needed, until chicken is very tender, about 2 hours.

Transfer chicken to a deep dish. Pour soup into a large jug or bowl. Cover and refrigerate chicken and soup for 6 to 8 hours.

Remove and discard the layer of fat that has solidified on the surface of soup. Pour soup into a large pot over medium heat; stir in corn and bring to a boil. Reduce heat and simmer until corn is tender, 10 to 15 minutes.

Meanwhile, place 2 eggs in a small saucepan and cover with cold water. Bring to a boil: remove from heat. Cover. Let eggs stand in hot water for 10 to 12 minutes. Cool, peel, and chop.

Chop chilled chicken meat into small chunks; stir into soup.

Beat remaining 1 egg in a medium bowl until light in color. Beat in flour and milk until smooth. Drop pea-sized lumps of rivel dough into the soup, a few at a time, to make small dumplings. Cook, stirring constantly, until dumplings hold their shape and float to the surface, 2 to 5 minutes. Stir in chopped egg.