Put carrots and celery in a saucepan. Add broth and pepper to the saucepan.
Put saucepan on burner. Turn the burner to high heat. Cook until mixture boils. Turn burner to medium-low heat. Put lid on saucepan and cook for 10 minutes. Use a wooden spoon to stir in the chicken.
Meanwhile, put the biscuit mix and milk in a bowl. Stir together with a large spoon.
Take lid off saucepan. For dumplings, spoon dough in 12 mounds on top of broth mixture. Put lid back on saucepan. Cook 10 minutes more or until a toothpick inserted into a dumpling comes out clean. Makes 6 servings.