Place chicken in a large stock pot and add water to barely cover it. Add 1 tsp salt, onion, celery, garlic, bay leaf, and parsley and stir. Bring to a boil, reduce heat to simmer, and cook covered for 1-2 hours.
Remove chicken from pot; set aside to cool. Add pepper, 1/2 tsp salt, and frozen veggies to the stock. Maintain the stock at a simmer.
Make the dumplings: combine the flour, baking powder, 2 tsp salt, and milk in a medium bowl, stirring until smooth. Let the dough rest 5-10 minutes. Place dough on a very well floured surface, and roll to about 1/2 inch thick.
Cut dough into 1/2-inch squares and drop individually into the simmering stock. Simmer 20-30 minutes, stirring often. Stock will thicken during this time.
Meanwhile, remove chicken from bones and cut or tear into bite-sized pieces. Return the chicken to the pot with the dumplings. Simmer until chicken is warmed through, and the "gravy" has thickened to desired consistency.
