Place the whole chicken or chicken parts into a large stockpot and cover with cold water. Add a few sprigs of thyme and a pinch of salt. Bring to a gentle simmer over medium heat, allowing the foam to rise and skim it off periodically.
Reduce the heat to maintain a gentle simmer and cook for about 1.5 hours, until the chicken is tender and falling apart. The broth will develop a rich aroma during this time.
Carefully remove the cooked chicken from the broth and set aside to cool slightly. Strain the broth through a fine-mesh strainer into another pot, discarding solids.
While the broth cools slightly, shred the chicken into bite-sized pieces using a sharp carving knife, discarding skin and bones if any.
Add chopped carrots, celery, and onion to the strained broth and bring to a gentle simmer. Cook until the vegetables are tender, about 10-15 minutes.
Stir in the minced garlic and cook for another 2 minutes until fragrant. Taste and season with salt and pepper as needed.
Return the shredded chicken to the pot, stirring to combine. Let everything simmer together for 5 minutes so flavors meld.
Add lemon zest and squeeze in lemon juice, stirring well to brighten the flavors. Toss in chopped parsley for freshness.
Adjust seasoning with additional salt, pepper, or lemon juice if desired. Remove the sprigs of thyme and discard.
Serve the hot chicken soup in bowls, garnished with extra parsley if desired. Enjoy the comforting aroma and hearty texture.
