Place the whole chicken or chicken pieces into a large stock pot and cover with cold water. Bring to a gentle simmer over medium heat, skimming off any foam that rises to the surface for the first 10 minutes. This helps keep the broth clear and clean.
Once the foam is skimmed, add the quartered onions, sliced carrots, celery, minced garlic, sprigs of thyme, and a pinch of salt. Turn the heat down to low and let everything simmer gently for about 1.5 hours, until the chicken is tender and the broth is fragrant.
Check the chicken’s internal temperature using a meat thermometer; it should reach 75°C (165°F). Carefully remove the chicken from the broth using a slotted spoon and set aside to cool slightly.
Strain the broth through a fine sieve into another pot or bowl, discarding the vegetable solids and herbs. Return the clear broth to the stove and bring it back to a gentle simmer.
While the broth heats, shred the cooked chicken into bite-sized pieces, discarding the skin and bones. Add the shredded chicken back into the simmering broth along with the sliced carrots and chopped parsley.
Finish the soup by squeezing fresh lemon juice into the broth, adjusting salt, and pepper to taste. Let it simmer for another 10 minutes so all flavors meld and vegetables soften just slightly.
Serve the chicken soup hot, garnished with extra parsley if desired, and enjoy the comforting, layered flavors of this homemade broth.