Warm the olive oil in a large soup pot over medium heat.
Add the sliced carrots, parsnips, celery, leek, and diced onion and cook them, stirring often, until they start to soften, approximately 4 to 5 minutes.
Mix in the minced garlic along with the salt and pepper, stirring continuously for about one minute until fragrant.
Tuck in the thyme, tarragon, bay leaf, whole chicken breasts, and pour the chicken broth into the pot.
Bring the mixture to a boil, then lower the heat to a gentle simmer and cover the pot.
Allow the soup to cook for 15 minutes, or until the chicken is thoroughly cooked through.
Remove the chicken breasts carefully using tongs and place on a cutting board.
Shred the chicken by pulling it apart with two forks.
Return the shredded chicken to the pot and let it simmer for another 1 to 2 minutes to meld flavors.
Discard the herb sprigs and bay leaf, then stir in the fresh parsley.
Serve the soup garnished with extra parsley and a dash of black pepper to taste.