Bring the chicken stock just to barely a boil in a large heavy soup pot.
Tie the herbs together with kitchen string and add to the pot with the chicken breast and chicken back if using.
Make sure the stock doesn't boil, if you have an instant-read thermometer you are looking for the temperature of the liquid to be 180F/82C.
Prep the vegetables while the chicken is cooking.
Poach the chicken for up to 30 minutes, or until chicken is cooked. It should be 165F/75C inside. Use tongs to remove chicken and herb bundle, setting chicken to cool on a cutting board and composting the herb bundle.
Turn up the heat to just barely boiling, add the vegetables and cook until fork tender, about 10 minutes. Turn off the heat.
Once chicken is cool enough to handle, remove skin, bones, and cartilage (saving in the freezer for a future pot of stock), and dice.
Add chicken to soup. Ladle soup into bowls and stir about 2 tbsp chopped parsley into each serving.
You can add the remaining parsley to the soup and store in the fridge, or leave it separate and add just before serving hot soup.