In a Dutch oven coated with cooking spray, cook and stir celery and carrots over medium heat until tender, about 5 minutes. Stir in broth, chicken and seasonings. Bring to a boil; reduce heat to a gentle simmer.
For dumplings, mix biscuit mix and milk until a soft dough forms. Drop by tablespoonfuls on top of the simmering liquid. Reduce heat to low; cover and cook until a toothpick inserted in dumplings comes out clean (do not lift cover during the first 10 minutes), 10-15 minutes.