Place chicken, celery, onion, bay leaves, bouillon cubes, and house seasoning in a large pot with 4 quarts of water.
Bring to a simmer over medium heat and cook until chicken is tender and thigh juices run clear, about 40 minutes.
Remove chicken from pot and let cool until safe to handle. Remove skin and separate meat from bones, then return chicken meat to the pot.
Keep chicken mixture warm over low heat while preparing dumplings.
For dumplings, mix flour and salt in a bowl, creating a mound in the center.
Gradually drizzle ice water over flour, starting from the center and working outward with your fingers to incorporate about ¾ cup ice water.
Knead dough into a ball, then roll out on a well-floured surface to ⅛-inch thickness. Let dough relax for several minutes.
Add cream of celery soup to the pot with chicken and simmer gently over medium-low heat.
Cut dough into 1-inch pieces. Pull each piece in half and drop into simmering soup.
Do not stir once dumplings are added. Instead, gently move the pot in a circular motion to submerge dumplings evenly.
Cook until dumplings float and are no longer doughy, 3-4 minutes.
Ladle into warm bowls and serve immediately.