Melt soup butter in a large wide pot and cook onion, carrots and celery for 6 minutes. Stir in soup flour for 1 minute, then gradually add broth.
Add chicken, soup salt, thyme and pepper and simmer gently for 12 minutes.
Whisk dumpling flour, baking powder and dumpling salt in a bowl. Stir in milk and melted dumpling butter just until a soft, slightly rough dough forms.
Drop the dough over the simmering soup in 12 small mounds, leaving gaps between them. Cover tightly and cook at a gentle simmer for 15 minutes without lifting the lid.
Check one dumpling: its center should be fluffy rather than wet dough and reach 160°F; the chicken must reach 165°F. Cover and cook for 2 to 3 minutes more if needed, then serve two dumplings with each bowl of soup.