Preheat oven to 350°.
In a large saucepan, saute onion and celery in butter until tender.
Stir in cream of mushroom soup, salt, and pepper until blended.
Gradually add broth; bring to a boil.
Cook and stir 1 minute or until thickened; reduce heat.
Add peas and carrots and cook 5 minutes, stirring constantly.
Stir in chicken. Pour into a greased 13x9-in. baking dish.
For dumplings, in a small bowl, combine baking mix and milk. Stir with a fork until moistened. Drop by tablespoonfuls into mounds over chicken mixture.
Bake, uncovered, 30 minutes.
Cover and bake 10 minutes longer or until a toothpick inserted in a dumpling comes out clean.