Old-Fashioned Southern Chicken and Dumplings

Name: Old-Fashioned Southern Chicken and Dumplings
Prep time: 30 min
Cook time: 1 h 20 min
Total time: 1 h 50 min
Cuisine: American, Southern
Ingredients: 1 (3 to 4-pound) whole young chicken; 3 ribs celery (each cut into 3 large pieces); 1 large onion (peeled and quartered); 1 tablespoon chicken base (like Better Than Bouillon - or 3 chicken bouillon cubes); 2 teaspoons salt; 1 teaspoon black pepper; 2 cups all-purpose flour (see note); 3/4 cup ice water; 1 (10.5-ounce) can cream of chicken soup; 3 tablespoons cornstarch (optional)