Place the whole chicken in a large heavy-bottomed pot and cover with cold water. Bring to a gentle simmer over medium heat, skimming off any foam that rises to the surface to keep the broth clear.
Add chopped onions, minced garlic, sliced carrots, celery, and thyme sprigs into the pot. Continue simmering gently for about 1.5 hours, allowing the flavors to meld and the chicken to become tender.
Remove the chicken from the broth and set aside to cool slightly. Strain the broth through a fine mesh strainer into another pot or bowl to remove all solids, resulting in a clear, flavorful base.
While the chicken cools, shred the meat into bite-sized pieces using two forks, discarding the skin and bones.
Return the strained broth to the stove and bring to a gentle simmer. Add the shredded chicken, chopped parsley, and season with salt and pepper to taste. Let everything simmer together for another 20 minutes, allowing the flavors to develop.
Taste the soup and adjust the seasoning with more salt, pepper, or herbs as desired. Serve hot, garnished with additional parsley if you like, alongside crusty bread for a complete meal.