Add celery, chicken breasts, onion, and chicken broth to the pot over medium heat. Let the mixture simmer for 15 minutes until the chicken is cooked. Remove from the broth and shred or chop the chicken using a sharp knife. Remove the pot from the heat and discard the onions and celery from the broth.

To a mixing bowl, add flour, salt, and baking powder. Mix them and then add milk. Whisk the mixture to make a shaggy dough. Cut this dough into 2-inch thick strips and add these strips into the simmering broth. Let these dumplings cook for about 30 minutes in the broth until the broth has a gravy-like thick consistency.

While the dumplings are simmering into hot broth, add the shredded chicken and season with salt and pepper. The Cracker Barrel chicken and dumplings are ready to serve.